hypothesis based problem solving examples

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• Who’s Joe?

“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found effective.”

– Edward Teller, Nuclear Physicist

During my first brainstorming meeting on my first project at McKinsey, this very serious partner, who had a PhD in Physics, looked at me and said, “So, Joe, what are your main hypotheses.” I looked back at him, perplexed, and said, “Ummm, my what?” I was used to people simply asking, “what are your best ideas, opinions, thoughts, etc.” Over time, I began to understand the importance of hypotheses and how it plays an important role in McKinsey’s problem solving of separating ideas and opinions from facts.

What is a Hypothesis?

“Hypothesis” is probably one of the top 5 words used by McKinsey consultants. And, being hypothesis-driven was required to have any success at McKinsey. A hypothesis is an idea or theory, often based on limited data, which is typically the beginning of a thread of further investigation to prove, disprove or improve the hypothesis through facts and empirical data.

The first step in being hypothesis-driven is to focus on the highest potential ideas and theories of how to solve a problem or realize an opportunity.

Let’s go over an example of being hypothesis-driven.

Let’s say you own a website, and you brainstorm ten ideas to improve web traffic, but you don’t have the budget to execute all ten ideas. The first step in being hypothesis-driven is to prioritize the ten ideas based on how much impact you hypothesize they will create.

The second step in being hypothesis-driven is to apply the scientific method to your hypotheses by creating the fact base to prove or disprove your hypothesis, which then allows you to turn your hypothesis into fact and knowledge. Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing:

1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost

While there are many other ways to validate the hypothesis on your prioritization , I find most people do not take this critical step in validating a hypothesis. Instead, they apply bad logic to many important decisions . An idea pops into their head, and then somehow it just becomes a fact.

One of my favorite lousy logic moments was a CEO who stated,

“I’ve never heard our customers talk about price, so the price doesn’t matter with our products , and I’ve decided we’re going to raise prices.”

Luckily, his management team was able to do a survey to dig deeper into the hypothesis that customers weren’t price-sensitive. Well, of course, they were and through the survey, they built a fantastic fact base that proved and disproved many other important hypotheses.

Why is being hypothesis-driven so important?

Imagine if medicine never actually used the scientific method. We would probably still be living in a world of lobotomies and bleeding people. Many organizations are still stuck in the dark ages, having built a house of cards on opinions disguised as facts, because they don’t prove or disprove their hypotheses. Decisions made on top of decisions, made on top of opinions, steer organizations clear of reality and the facts necessary to objectively evolve their strategic understanding and knowledge. I’ve seen too many leadership teams led solely by gut and opinion. The problem with intuition and gut is if you don’t ever prove or disprove if your gut is right or wrong, you’re never going to improve your intuition. There is a reason why being hypothesis-driven is the cornerstone of problem solving at McKinsey and every other top strategy consulting firm.

How do you become hypothesis-driven?

Most people are idea-driven, and constantly have hypotheses on how the world works and what they or their organization should do to improve. Though, there is often a fatal flaw in that many people turn their hypotheses into false facts, without actually finding or creating the facts to prove or disprove their hypotheses. These people aren’t hypothesis-driven; they are gut-driven.

The conversation typically goes something like “doing this discount promotion will increase our profits” or “our customers need to have this feature” or “morale is in the toilet because we don’t pay well, so we need to increase pay.” These should all be hypotheses that need the appropriate fact base, but instead, they become false facts, often leading to unintended results and consequences. In each of these cases, to become hypothesis-driven necessitates a different framing.

• Instead of “doing this discount promotion will increase our profits,” a hypothesis-driven approach is to ask “what are the best marketing ideas to increase our profits?” and then conduct a marketing experiment to see which ideas increase profits the most.

• Instead of “our customers need to have this feature,” ask the question, “what features would our customers value most?” And, then conduct a simple survey having customers rank order the features based on value to them.

• Instead of “morale is in the toilet because we don’t pay well, so we need to increase pay,” conduct a survey asking, “what is the level of morale?” what are potential issues affecting morale?” and what are the best ideas to improve morale?”

Beyond, watching out for just following your gut, here are some of the other best practices in being hypothesis-driven:

Listen to Your Intuition

Your mind has taken the collision of your experiences and everything you’ve learned over the years to create your intuition, which are those ideas that pop into your head and those hunches that come from your gut. Your intuition is your wellspring of hypotheses. So listen to your intuition, build hypotheses from it, and then prove or disprove those hypotheses, which will, in turn, improve your intuition. Intuition without feedback will over time typically evolve into poor intuition, which leads to poor judgment, thinking, and decisions.

Constantly Be Curious

I’m always curious about cause and effect. At Sports Authority, I had a hypothesis that customers that received service and assistance as they shopped, were worth more than customers who didn’t receive assistance from an associate. We figured out how to prove or disprove this hypothesis by tying surveys to transactional data of customers, and we found the hypothesis was true, which led us to a broad initiative around improving service. The key is you have to be always curious about what you think does or will drive value, create hypotheses and then prove or disprove those hypotheses.

Validate Hypotheses

You need to validate and prove or disprove hypotheses. Don’t just chalk up an idea as fact. In most cases, you’re going to have to create a fact base utilizing logic, observation, testing (see the section on Experimentation ), surveys, and analysis.

Be a Learning Organization

The foundation of learning organizations is the testing of and learning from hypotheses. I remember my first strategy internship at Mercer Management Consulting when I spent a good part of the summer combing through the results, findings, and insights of thousands of experiments that a banking client had conducted. It was fascinating to see the vastness and depth of their collective knowledge base. And, in today’s world of knowledge portals, it is so easy to disseminate, learn from, and build upon the knowledge created by companies.

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Career in Consulting

Hypothesis-driven approach: the definitive guide

Imagine you are walking in one of McKinsey’s offices.

Around you, there are a dozen of busy consultants.

The word “hypothesis” would be one of the words you would hear the most.

Along with “MECE” or “what’s the so-what?”.

This would also be true in any BCG, Bain & Company office or other major consulting firms.

Because strategy consultants are trained to use a hypothesis-driven approach to solve problems.

And as a candidate, you must demonstrate your capacity to be hypothesis-driven in your case interviews .

There is no turnaround:

If you want a consulting offer, you MUST know how to use a hypothesis-driven approach .

Like a consultant would be hypothesis-driven on a real project for a real client?

Hell, no! Big mistake!

Because like any (somehow) complex topics in life, the context matters.

What is correct in one context becomes incorrect if the context changes.

And this is exactly what’s happening with using a hypothesis-driven approach in case interviews.

This should be different from the hypothesis-driven approach used by consultant solving a problem for a real client .

And that’s why many candidates get it wrong (and fail their interviews).

They use a hypothesis-driven approach like they were already a consultant.

Thus, in this article, you’ll learn the correct definition of being hypothesis-driven in the context of case interviews .

Plus, you’ll learn how to use a hypothesis in your case interviews to “crack the case”, and more importantly get the well-deserved offer!

Ready? Let’s go. It will be super interesting!

Table of Contents

The wrong hypothesis-driven approach in case interviews.

Let’s start with a definition:

Hypothesis-driven thinking is a problem-solving method whereby you start with the answer and work back to prove or disprove that answer through fact-finding.

Concretely, here is how consultants use a hypothesis-driven approach to solve their clients’ problems:

• Form an initial hypothesis, which is what they think the answer to the problem is.
• Craft a logic issue tree , by asking themselves “what needs to be true for the hypothesis to be true?”
• Walk their way down the issue tree and gather the necessary data to validate (or refute) the hypothesis.
• Reiterate the process from step 1 – if their first hypothesis was disproved by their analysis – until they get it right.

With this answer-first approach, consultants do not gather data to fish for an answer. They seek to test their hypotheses , which is a very efficient problem-solving process.

The answer-first thinking works well if the initial hypothesis has been carefully formed.

This is why – in top consulting firms like McKinsey , BCG , or Bain & Company – the hypothesis is formed by a Partner with 20+ years of work experience.

And this is why this is NOT the right approach for case interviews.

Imagine a candidate doing a case interview at McKinsey and using answer-first thinking.

At the beginning of a case, this candidate forms a hypothesis (a potential answer to the problem), builds a logic tree, and gathers data to prove the hypothesis.

Here, there are two options:

The initial hypothesis is right

The initial hypothesis is wrong

If the hypothesis is right, what does it mean for the candidate?

That the candidate was lucky.

Nothing else.

And it certainly does not prove the problem-solving skills of this candidate (which is what is tested in case interviews).

Now, if the hypothesis is wrong, what’s happening next?

The candidate reiterates the process.

Imagine how disorganized the discussion with the interviewer can be.

Most of the time, such candidates cannot form another hypothesis, the case stops, and the candidate feels miserable.

This leads us to the right hypothesis-driven approach for case interviews.

The right hypothesis-driven approach in case interviews

To make my point clear between the wrong and right approach, I’ll take a non-business example.

Let’s imagine you want to move from point A to point B.

And for that, you have the choice among a multitude of roads.

Using the answer-first approach presented in the last section, you’d know which road to take to move from A to B (for instance the red line in the drawing below).

Again, this would not demonstrate your capacity to find the “best” road to go from A to B.

(regardless of what “best” means. It can be the fastest or the safest for instance.)

Now, a correct hypothesis-driven approach consists in drawing a map with all the potential routes between A and B, and explaining at each intersection why you want to turn left or right (” my hypothesis is that we should turn right ”).

And in the context of case interviews?

In the above analogy:

• A is the problem
• B is the solution
• All the potential routes are the issues in your issue tree

And the explanation of why you want to take a certain road instead of another would be your hypothesis.

Is the difference between the wrong and right hypothesis-driven approach clearer?

If not, don’t worry. You’ll find many more examples below in this article.

But, next, let’s address another important question.

Why you must (always) use a hypothesis in your case interviews

You must use a hypothesis in your case interviews for two reasons.

A hypothesis helps you focus on what’s important to solve the case

Using a hypothesis-driven approach is critical to solving a problem efficiently.

In other words:

A hypothesis will limit the number of analysis you need to perform to solve a problem.

Thus, this is a way to apply the 80/20 principle and prioritize the issues (from your MECE issue tree ) you want to investigate.

And this is very important because your time with your interviewer is limited (like is the time with your client on a real project).

Let’s take a simple example of a hypothesis:

The profits of your client have dropped.

And your initial analysis shows increasing costs and stagnating revenues.

So your hypothesis can be:

“I think something happened in our cost structure, causing the profit drop. Next, I’d like to understand better the cost structure of our clients and which cost items have changed recently.”

Here the candidate is rigorously “cutting” half of his/her issue tree (the revenue side) and will focus the case discussion on the cost side.

And this is a good example of a hypothesis in case interviews.

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A hypothesis tells your interviewers why you want to do an analysis

There is a road that you NEVER want to take.

On this road, the purpose of the questions asked by a candidate is not clear.

Here are a few examples:

“What’s the market size? growth?”

“Who are the main competitors? what are their market shares?”

“Have customer preferences changed in this market?”

This list of questions might be relevant to solve the problem at stake.

But how these questions help solve the problem is not addressed.

Or in other words, the logical connection between these questions and the problem needs to be included.

So, a better example would be:

“We discovered that our client’s sales have declined for the past three years. I would like to know if this is specific to our client or if the whole market has the same trend. Can you tell me how the market size has changed over the past three years? »

In the above question, the reason why the candidate wants to investigate the market is clear: to narrow down the analysis to an internal root cause or an external root cause.

Yet, I see only a few (great) candidates asking clear and purposeful questions.

You want to be one of these candidates.

How to use a hypothesis-driven approach in your case interviews?

At this stage, you understand the importance of a hypothesis-driven approach in case interviews:

You want to identify the most promising areas to analyze (remember that time is money ).

And there are two (and only two) ways to create a good hypothesis in your case interviews:

• a quantitative way
• a qualitative way

Let’s start with the quantitative way to develop a good hypothesis in your case interviews.

The quantitative approach: use the available data

Let’s use an example to understand this data-driven approach:

Interviewer: your client is manufacturing computers. They have been experiencing increasing costs and want to know how to address this issue.

Candidate: to begin with, I want to know the breakdown of their cost structure. Do you have information about the % breakdown of their costs?

Interviewer: their materials costs count for 30% and their manufacturing costs for 60%. The last 10% are SG&A costs.

Candidate: Given the importance of manufacturing costs, I’d like to analyze this part first. Do we know if manufacturing costs go up?

Interviewer: yes, manufacturing costs have increased by 20% over the past 2 years.

Candidate: interesting. Now, it would be interesting to understand why such an increase happened.

You can notice in this example how the candidate uses data to drive the case discussion and prioritize which analysis to perform.

The candidate made a (correct) hypothesis that the increasing costs were driven by the manufacturing costs (the biggest chunk of the cost structure).

Even if the hypothesis were incorrect, the candidate would have moved closer to the solution by eliminating an issue (manufacturing costs are not causing the overall cost increase).

That said, there is another way to develop a good hypothesis in your case interviews.

The qualitative approach: use your business acumen

Sometimes you don’t have data (yet) to make a good hypothesis.

Thus, you must use your business judgment and develop a hypothesis.

Again, let’s take an example to illustrate this approach.

Interviewer: your client manufactures computers and has been losing market shares to their direct competitors. They hired us to find the root cause of this problem.

Candidate: I think of many reasons explaining the drop in market shares. First, our client manufactures and sells not-competitive products. Secondly, we might price our products too high. Third, we need to use the right distribution channels. For instance, we might sell in brick-and-mortars stores when consumers buy their computers in e-stores like Amazon. Finally, I think of our marketing expenses. There may be too low or not used strategically.

Candidate: I see these products as commodities where consumers use price as the main buying decision criteria. That’s why I’d like to explore how our client prices their products. Do you have information about how our prices compare to competitors’?

Interviewer: this is a valid point. Here is the data you want to analyze.

Note how this candidate explains what she/he wants to analyze first (prices) and why (computers are commodities).

In this case interview, the hypothesis-driven approach looks like this:

This is a commodity industry —> consumers buying behavior is driven by pricing —> our client’s prices are too high.

Again, note how the candidate first listed the potential root causes for this situation and did not use an answer-first approach.

Want to learn more?

In this free training , I explain in detail how to use data or your business acumen to prioritize the issues to analyze and “crack the case.”

Also, you’ll learn what to do if you don’t have data or can’t use your business acumen.

Sign up now for free .

Form a hypothesis in these two critical moments of your case interviews

After you’ve presented your initial structure.

The first moment to form a hypothesis in your case interview?

In the beginning, after you’ve presented your structure.

When you’ve presented your issue tree, mention which issue you want to analyze first.

Also, explain why you want to investigate this first issue.

Make clear how the outcome of the analysis of this issue will help you solve the problem.

After an analysis

The second moment to form a hypothesis in your case interview?

After you’ve derived an insight from data analysis.

This insight has proved (or disproved) your hypothesis.

Either way, after you have developed an insight, you must form a new hypothesis.

This can be the issue you want to analyze next.

Or what a solution to the problem is.

Hypothesis-driven approach in case interviews: a conclusion

Having spent about 10 years coaching candidates through the consulting recruitment process , one commonality of successful candidates is that they truly understand how to be hypothesis-driven and demonstrate efficient problem-solving.

Plus, per my experience in coaching candidates , not being able to use a hypothesis is the second cause of rejection in case interviews (the first being the lack of MECEness ).

This means you can’t afford NOT to master this concept in a case study.

So, sign up now for this free course to learn how to use a hypothesis-driven approach in your case interviews and land your dream consulting job.

More than 7,000 people have already signed up.

Don’t waste one more minute!

See you there.

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Hypothesis Based Problem Solving

Problem-solving using a hypothesis-based approach.

Thinking back to my days of doing puzzles and quizzes, I remembered doing mazes. Just how did I get to the prize in the middle? Well, I always cheated. I started at the end and worked backwards, and it was still much more comfortable.

The same can be said of problem-solving. Think about the endpoint (solution) and work back from there. That is the principle of a hypothesis-based approach.

What is the hypothesis?

Hypothesis – an idea suggested as a possible explanation for a particular situation or condition but has not yet been proved correct – source Collins Dictionary.

What is problem-solving using a hypothesis-based approach?

Firstly we need to define with precision what the problem/opportunity is?

Write it down and gain agreement that this is the issue.

To help clarify, use the 5 Whys tool and check that the problem is the problem (industrialist Sakichi Toyoda developed the 5 Whys). It ensures that you understand the root cause, not just the symptoms, i.e. what you can ‘see’ (particularly useful if you have a recurring problem). At each ‘Why’, you will identify potential courses of action. However, a thorny issue may require a more complex approach.

It is a simple technique often used by 5-year-olds when they don’t like the answer you have just given them…

Develop an action plan

What are we going to do? Who is going to do it? When will it be completed? Are there any dependencies? What do we already know? What don’t we know?

Analyse the data available. Use the data to test our hypothesis. Does this back up our belief?

Are the gaps significant? Do we need to buy/commission more data? Run trials?

Be strict, ask yourself, “what question am I trying to answer?”

Update the action plan and go back around the loop based on the findings or impact on timings. Confirm or amend hypotheses.

Using a hypothesis-based approach to problem-solving should deliver results quicker and with a better return. It is an efficient way to validate/create solutions, reduce time spent on aimless analysis, and more time on research to deliver results.

What are the potential explanations? What are our hypotheses?

Don’t re-invent the wheel. The answer may already be ‘known’, i.e. a hypothesis. Gather a group together and work through the potential solutions to solve the problem / deliver the opportunity. Throw out any that are not plausible based on knowledge /experience.

You can use a logic/issue tree to capture the parts.

Prioritise. How big is each solution (if relevant)? How will it contribute to solving the problem? What will it cost, and how long will it take? Identify the answers you want to take forward, break them down into parts so that actions/responsibility can be divided and allocated. Remember the 80:20 rule too. Identify some easy wins and some more complicated steps.

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How to Implement Hypothesis-Driven Development

Remember back to the time when we were in high school science class. Our teachers had a framework for helping us learn – an experimental approach based on the best available evidence at hand. We were asked to make observations about the world around us, then attempt to form an explanation or hypothesis to explain what we had observed. We then tested this hypothesis by predicting an outcome based on our theory that would be achieved in a controlled experiment – if the outcome was achieved, we had proven our theory to be correct.

We could then apply this learning to inform and test other hypotheses by constructing more sophisticated experiments, and tuning, evolving or abandoning any hypothesis as we made further observations from the results we achieved.

Experimentation is the foundation of the scientific method, which is a systematic means of exploring the world around us. Although some experiments take place in laboratories, it is possible to perform an experiment anywhere, at any time, even in software development.

Practicing  Hypothesis-Driven Development  is thinking about the development of new ideas, products and services – even organizational change – as a series of experiments to determine whether an expected outcome will be achieved. The process is iterated upon until a desirable outcome is obtained or the idea is determined to be not viable.

We need to change our mindset to view our proposed solution to a problem statement as a hypothesis, especially in new product or service development – the market we are targeting, how a business model will work, how code will execute and even how the customer will use it.

We do not do projects anymore, only experiments. Customer discovery and Lean Startup strategies are designed to test assumptions about customers. Quality Assurance is testing system behavior against defined specifications. The experimental principle also applies in Test-Driven Development – we write the test first, then use the test to validate that our code is correct, and succeed if the code passes the test. Ultimately, product or service development is a process to test a hypothesis about system behaviour in the environment or market it is developed for.

The key outcome of an experimental approach is measurable evidence and learning.

Learning is the information we have gained from conducting the experiment. Did what we expect to occur actually happen? If not, what did and how does that inform what we should do next?

In order to learn we need use the scientific method for investigating phenomena, acquiring new knowledge, and correcting and integrating previous knowledge back into our thinking.

As the software development industry continues to mature, we now have an opportunity to leverage improved capabilities such as Continuous Design and Delivery to maximize our potential to learn quickly what works and what does not. By taking an experimental approach to information discovery, we can more rapidly test our solutions against the problems we have identified in the products or services we are attempting to build. With the goal to optimize our effectiveness of solving the right problems, over simply becoming a feature factory by continually building solutions.

The steps of the scientific method are to:

• Make observations
• Formulate a hypothesis
• Design an experiment to test the hypothesis
• State the indicators to evaluate if the experiment has succeeded
• Conduct the experiment
• Evaluate the results of the experiment
• Accept or reject the hypothesis
• If necessary, make and test a new hypothesis

Using an experimentation approach to software development

We need to challenge the concept of having fixed requirements for a product or service. Requirements are valuable when teams execute a well known or understood phase of an initiative, and can leverage well understood practices to achieve the outcome. However, when you are in an exploratory, complex and uncertain phase you need hypotheses.

Handing teams a set of business requirements reinforces an order-taking approach and mindset that is flawed.

Business does the thinking and ‘knows’ what is right. The purpose of the development team is to implement what they are told. But when operating in an area of uncertainty and complexity, all the members of the development team should be encouraged to think and share insights on the problem and potential solutions. A team simply taking orders from a business owner is not utilizing the full potential, experience and competency that a cross-functional multi-disciplined team offers.

Framing hypotheses

The traditional user story framework is focused on capturing requirements for what we want to build and for whom, to enable the user to receive a specific benefit from the system.

As A…. <role>

I Want… <goal/desire>

So That… <receive benefit>

Behaviour Driven Development (BDD) and Feature Injection  aims to improve the original framework by supporting communication and collaboration between developers, tester and non-technical participants in a software project.

In Order To… <receive benefit>

As A… <role>

When viewing work as an experiment, the traditional story framework is insufficient. As in our high school science experiment, we need to define the steps we will take to achieve the desired outcome. We then need to state the specific indicators (or signals) we expect to observe that provide evidence that our hypothesis is valid. These need to be stated before conducting the test to reduce biased interpretations of the results. 

If we observe signals that indicate our hypothesis is correct, we can be more confident that we are on the right path and can alter the user story framework to reflect this.

Therefore, a user story structure to support Hypothesis-Driven Development would be;

We believe < this capability >

What functionality we will develop to test our hypothesis? By defining a ‘test’ capability of the product or service that we are attempting to build, we identify the functionality and hypothesis we want to test.

Will result in < this outcome >

What is the expected outcome of our experiment? What is the specific result we expect to achieve by building the ‘test’ capability?

We will know we have succeeded when < we see a measurable signal >

What signals will indicate that the capability we have built is effective? What key metrics (qualitative or quantitative) we will measure to provide evidence that our experiment has succeeded and give us enough confidence to move to the next stage.

The threshold you use for statistically significance will depend on your understanding of the business and context you are operating within. Not every company has the user sample size of Amazon or Google to run statistically significant experiments in a short period of time. Limits and controls need to be defined by your organization to determine acceptable evidence thresholds that will allow the team to advance to the next step.

For example if you are building a rocket ship you may want your experiments to have a high threshold for statistical significance. If you are deciding between two different flows intended to help increase user sign up you may be happy to tolerate a lower significance threshold.

The final step is to clearly and visibly state any assumptions made about our hypothesis, to create a feedback loop for the team to provide further input, debate and understanding of the circumstance under which we are performing the test. Are they valid and make sense from a technical and business perspective?

Hypotheses when aligned to your MVP can provide a testing mechanism for your product or service vision. They can test the most uncertain areas of your product or service, in order to gain information and improve confidence.

Examples of Hypothesis-Driven Development user stories are;

Business story

We Believe That increasing the size of hotel images on the booking page

Will Result In improved customer engagement and conversion

We Will Know We Have Succeeded When we see a 5% increase in customers who review hotel images who then proceed to book in 48 hours.

It is imperative to have effective monitoring and evaluation tools in place when using an experimental approach to software development in order to measure the impact of our efforts and provide a feedback loop to the team. Otherwise we are essentially blind to the outcomes of our efforts.

In agile software development we define working software as the primary measure of progress.

By combining Continuous Delivery and Hypothesis-Driven Development we can now define working software and validated learning as the primary measures of progress.

Ideally we should not say we are done until we have measured the value of what is being delivered – in other words, gathered data to validate our hypothesis.

Examples of how to gather data is performing A/B Testing to test a hypothesis and measure to change in customer behaviour. Alternative testings options can be customer surveys, paper prototypes, user and/or guerrilla testing.

One example of a company we have worked with that uses Hypothesis-Driven Development is  lastminute.com . The team formulated a hypothesis that customers are only willing to pay a max price for a hotel based on the time of day they book. Tom Klein, CEO and President of Sabre Holdings shared  the story  of how they improved conversion by 400% within a week.

Combining practices such as Hypothesis-Driven Development and Continuous Delivery accelerates experimentation and amplifies validated learning. This gives us the opportunity to accelerate the rate at which we innovate while relentlessly reducing cost, leaving our competitors in the dust. Ideally we can achieve the ideal of one piece flow: atomic changes that enable us to identify causal relationships between the changes we make to our products and services, and their impact on key metrics.

As Kent Beck said, “Test-Driven Development is a great excuse to think about the problem before you think about the solution”. Hypothesis-Driven Development is a great opportunity to test what you think the problem is, before you work on the solution.

How can you achieve faster growth?

Solving Problems with the Hypothesis-based Approach

• Post author By Jason Oh
• Post date June 17, 2023
• 1 Comment on Solving Problems with the Hypothesis-based Approach

There are generally two main approaches to solving problems in consulting, namely the:

• Investigative / data-based approach, and
• Hypothesis-based approach.

The investigative approach is appropriate when the opportunity is well-defined, repetitive, and standardized, or where the solution is clear from the beginning. Progress is made by employing technical and subject matter expertise to drive towards the solution. For example, implementing new IT software for a business unit.

The investigative approach generally involves:

• Collecting and analyzing data
• Understanding key issues
• Identifying and developing solutions

In contrast, the hypothesis-based approach to problem solving is appropriate where the opportunity is unstructured and unique and does not have an obvious solution. Progress is made by employing systematic problem-solving skills to validate an initial premise and circle in on the root cause of the issue before proposing possible solutions. For example, the enterprise may be facing a profitability decline and needs to conduct a strategic assessment.

The hypothesis-based approach generally involves:

• Using deep experience of the industry, organization, and issues
• Developing one or more initial hypotheses about the real problem and possible solutions
• Identifying data and analysis needed to prove or disprove the hypothesis

Investigative vs Hypothesis-based Approach

Here is a summary of the advantages and challenges of the investigative versus the hypothesis-based approach.

Clients pay consultants to give them valuable insights and do this quickly. As such, consultants tend to employ the hypothesis-based approach wherever they can. Since leading consulting firms typically have extensive industry experience, this helps consultants to focus on the most likely problem and solution areas. This ensures that all data gathering and analysis has a clear purpose and time is not wasted doing aimless work.

Hypothesis-based Problem-Solving Approach

The hypothesis-based problem solving (HBPS) approach is a framework used in strategy consulting to develop insights and recommendations based on a structured, evidence-based process.

The HBPS process has five key steps.

1. Define the problem

Defining the problem is critical to the success of the HBPS approach. This involves understanding the broader context by engaging with the client to gain an understanding of the challenges they are facing. This might also involve conducting interviews with key stakeholders, reviewing relevant documents and data, and conducting market research to understand the situation.

Once the context is adequately understood, the consultant will need to define the scope and objectives of the engagement. This might involve drafting a written proposal that outlines the scope of the engagement, key deliverables, and the timeline for completion.

2. Define drivers and generate/refine hypotheses

Defining drivers involves identifying factors that contribute to the situation at hand. For example, if a company is experiencing declining sales, the drivers might include changes in consumer behaviour, increased competition, or a decline in product quality. To identify potential drivers, consultants will typically conduct research, such as reviewing financial data, market research reports, or conducting surveys, focus groups, or interviews with key stakeholders.

Once potential drivers have been identified, consultants can then generate hypotheses about the impact of each driver on the problem. For example, “Increased competition is causing a decline in market share” or “Changes in consumer preferences are reducing demand for the client’s product”.

3. Determine information needs

Identifying the required data sources requires reviewing the hypotheses and identifying the types of data required to test them. This might include financial data, market research, or customer feedback.

Consultants will also need to work with the client to develop a plan for collecting and analyzing the data. In developing this plan, consultants will need to ensure that the data to be collected is aligned with the scope and objectives of the engagement.

4. Gather and analyze the data

Collecting data from relevant sources might involve conducting primary research, such as surveys, interviews, or focus groups, or conducting secondary research, such as reviewing industry reports or analyzing financial data. In collecting the required data, consultants will need to ensure that the data is relevant, accurate, and comprehensive.

Analyzing the data to test the hypotheses might then involve conducting various forms of statistical and data analysis .

5. Draw conclusions and develop recommendations

Drawing conclusions requires evaluating the results of the data analysis. This involves identifying patterns, trends, or insights that emerge from the data.

Developing recommendations from the insights generated will require synthesizing the findings into actionable recommendations. These recommendations might include specific projects or initiatives that the client should undertake to address the problem faced, or might involve broader strategic recommendations related to the client’s business or industry. The consultants should ensure that recommendations are actionable, measurable, and realistic, and that they can be implemented within a particular timeframe and budget.

The bottom line

The two main approaches to problem-solving in consulting are the investigative/data-based approach and the hypothesis-based approach. The former can be used where the problem is well-defined, while the latter can be used when the problem is novel.

The hypothesis-based approach is generally more efficient and aims to get directly to the root of the problem. Clients pay consultants to give them valuable insights quickly, which is why consultants tend to employ the hypothesis-based approach.

The HBPS approach involves five key steps: defining the problem, generating hypotheses, determining information needs, gathering and analyzing the data, and developing recommendations based on the insights generated.

In the next article, we will explore the five key steps of the HBPS approach in greater detail.

Jason Oh is a Senior Associate at Strategy&. Previously, he was part of the Global Wealth & Asset Management Strategy team of a large financial institution and served EY and Novantas in their strategy consulting business with industry focus in the financial services sector.

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Consulting Hypothesis Tree: Everything You Need to Know

• Last Updated June, 2023

A hypothesis tree is a powerful problem-solving framework used by consultants. It takes your hypothesis, your best guess at the solution to your client’s problem, and breaks it down into smaller parts to prove or disprove. With a hypothesis tree, you can focus on what’s important without getting bogged down in details.

Are you feeling overwhelmed during a complex case interview? Try using a hypothesis tree! It’ll help you communicate your insights more effectively, increasing your chances of acing the case.

In this article, we’ll discuss:

• What a hypothesis tree is, and why it’s important in consulting interviews
• Differences between a hypothesis tree vs. an issue tree
• The structure of a hypothesis tree and how to construct one
• A hypothesis tree example
• Our 4 tips for using a hypothesis tree effectively in consulting interviews

Let’s get started!

Definition of a Hypothesis Tree and Why It's Important

6 steps to build a hypothesis tree, hypothesis tree example, 4 tips for using a hypothesis tree in your interview, limitations to using a hypothesis tree, other consulting concepts related to hypothesis trees.

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A hypothesis tree is a tool consultants use to tackle complex problems by organizing potential insights around a central hypothesis. It provides a structured framework for solving problems by forming sub-hypotheses that, if true, support the central hypothesis. This allows consultants to explore problems more effectively and communicate their insights.

Mastering the hypothesis tree can help you stand out in your case interview. It enables you to showcase your problem-solving skills and critical thinking ability by presenting insights and hypotheses in a concise and organized manner. This helps you avoid getting overwhelmed by the complexity of the client’s problem.

Hypothesis trees are not limited to consulting interviews; they are an essential tool in real-world consulting projects! At the beginning of a project, the partner in charge or the manager will create a hypothesis tree to scope the problem, identify potential solutions, and assign project roles. Acting as a “north star,” a hypothesis tree gives a clear direction for the team, aligning their efforts toward solving the problem. Throughout the project, the team can adapt and refine the hypothesis tree as new information emerges.

The terms “hypothesis tree” and “issue tree” are often used interchangeably in consulting. However, it’s important to understand their key differences.

Differences Between a Hypothesis Tree vs. an Issue Tree

A hypothesis tree is less flexible as it is based on a predetermined hypothesis or set of hypotheses. In contrast, an issue tree can be more flexible in its approach to breaking down a problem and identifying potential solutions.

Let’s look at a client problem and high-level solution frameworks to illustrate the differences: TelCo wants to expand to a new geography. How can we help our client determine their market entry strategy?

If you were to start building a hypothesis tree to explore  this, your hypothesis tree might include:

Hypothesis: TelCo should enter the new market.

• It has immense potential and is growing rapidly.
• The expansion is forecasted to be profitable as the costs to operate the service in the new market are low.
• There are few large competitors, and our product has a competitive advantage.
• How attractive is the new market? What is the growth outlook? What is the profitability forecast for this new market?
• What are the different customer segments?
• How is our client’s service differentiated from local competitors?

Nail the case & fit interview with strategies from former MBB Interviewers that have helped 89.6% of our clients pass the case interview.

Here are the 6 steps to build a hypothesis tree. Practice doing these in your mock case interviews!

1. Understand the Problem

Before building a hypothesis tree, you need to understand the problem thoroughly. Gather all the information and data related to the problem. In a case interview, ask clarifying questions after the interviewer has delivered the case problem to help you build a better hypothesis.

2. Brainstorm

Brainstorm and generate as many hypotheses as possible that could solve the problem. Ensure that the hypotheses are MECE. In your interview, you can ask for a few moments to write down your brainstorming before communicating them in a structured way.

3. Organize the Hypotheses

Once you have brainstormed, organize your thoughts into a structured hierarchy. Each hypothesis should be represented as a separate branch in the hierarchy, with supporting hypotheses below.

4. Evaluate the Hypotheses

Evaluate each hypothesis based on its feasibility, relevance, and potential impact on the problem. Eliminate any hypotheses that are unlikely to be valid or don’t provide significant value to the analysis. During your interview, focus on the highest likelihood solutions first. You will not have the time to go through all your hypotheses.

5. Test the Hypotheses

Test your central hypothesis by confirming or refuting each of the sub-hypotheses. If you need data to do this, ask your interviewer for it. Analyze any information you receive and interpret its impact on your hypothesis before moving on. Does it confirm or refute it?

If it refutes your hypothesis, don’t worry. That doesn’t mean you’ve botched your case interview. You just need to pivot to a new hypothesis based on this information.

6. Refine the Hypotheses

Refine the hypothesis tree as you learn more from data or exhibits. You might need to adjust your hypothesis or the structure of the hypothesis tree based on what you learn.

Let’s go back to the TelCo market entry example from earlier. 

Hypothesis : TelCo should enter the Indian market and provide internet service. 

Market Opportunity : The Indian market is attractive to TelCo.

• The Indian telecommunications market is growing rapidly, and there is room for another provider.
• Margins are higher than in TelCo’s other markets.
• The target customer segments are urban and rural areas with high population densities.
• The competition is low, and there is an opportunity for a new provider for customers who need reliable and affordable service.

Operational Capabilities : The company has the capacity and resources to operate in India.

• TelCo can leverage its existing expertise and technology to gain a competitive advantage.
• TelCo should build out its Indian operations to minimize costs and maximize efficiency.
• TelCo should consider investing in existing local infrastructure to ensure reliable service delivery.
• TelCo can explore alliances with technology content providers to offer value-added services to customers.

Regulatory Environment : The local regulators approve of a new provider entering the market.

• TelCo must ensure compliance with Indian telecommunications regulations.
• TelCo should also be aware of any upcoming regulatory changes that may impact its business operations.

Overall, this hypothesis tree can help guide the analysis and process to conclude if TelCo should enter the Indian market.

1. Develop Common Industry Knowledge

By familiarizing yourself with common industry problems and solutions, you can build a foundation of high-level industry knowledge to help you form relevant hypotheses during your case interviews. 

For example, in the mining industry, problems often revolve around declining profitability and extraction quality. Solutions may include reducing waste, optimizing resources, and exploring new sites. 

In retail banking, declining customer satisfaction and retention are common problems. Potential solutions are improving customer service, simplifying communication, and optimizing digital solutions.

Consulting club case books like this one from the Fuqua School of Business frequently have industry overviews you can refer to. 

2. Practice Building Hypothesis Trees

Building a hypothesis tree requires practice. Look for opportunities to practice generating hypotheses in everyday situations, such as when reading news articles or listening to podcasts. This will help you develop your ability to structure your thoughts and ideas quickly and naturally.

3. Use Frameworks to Guide Building a Hypothesis Tree

Remember, you can reference common business frameworks, such as the profitability formula, as inputs to your hypothesis. Use frameworks as a starting point, but don’t be afraid to deviate from them if it leads to a better hypothesis tree.

Interviewers expect candidates to tailor their approach to the specific client situation. Try to think outside the box and consider new perspectives that may not fit neatly into a framework. 

For an overview of common concepts, we have an article on Case Interview Frameworks .

4. Embrace Flexibility

Don’t be afraid to pivot your hypotheses and adjust your approach based on new data or insights. This demonstrates professionalism and openness to feedback, which are highly valued traits in consulting.

Although hypothesis trees are a helpful tool for problem-solving, they have limitations. 

The team’s expertise and understanding of the problem are crucial to generating a complete and accurate hypothesis. Relying on a hypothesis tree poses the risk of confirmation bias, as the team may unconsciously favor a solution based on past experiences. This is particularly risky in rapidly evolving industries, such as healthcare technology, where solutions that have worked for past clients may no longer be relevant due to regulatory changes.

A hypothesis tree can also be inflexible in incorporating new information mid-project. It may accidentally limit creativity if teams potentially overlook alternative solutions. 

It’s important to be aware of these limitations and use a hypothesis tree with other problem-solving methods.

Several concepts in consulting are related to hypothesis trees. They all provide a structure for problem-solving and analysis. Each has its unique strengths and applications, and consultants may use a combination of these concepts depending on the specific needs of the problem.

Let’s look at some concepts:

• Issue Trees : As mentioned earlier in the article, issue trees are similar to hypothesis trees, but instead of starting with a hypothesis, they start with a problem and break it down into smaller, more manageable issues. Issue trees are often used to identify a problem’s root cause and to prioritize which sub-issues to focus on. If you want to learn more, we have a detailed explanation of Issue Trees .
• MECE Structure : MECE stands for mutually exclusive, collectively exhaustive. It is used to organize information and ensure that all possible options are considered. It is often used in conjunction with a hypothesis tree to ensure that all potential hypotheses are considered and that there is no overlap in the analysis. For an overview of the MECE Case Structure , check out our article.
• Pyramid Principle : This is a communication framework for structuring presentations, such as case interviews. It starts with a hypothesis and three to four key arguments, each with supporting evidence. You can use it throughout the case for structuring and communicating ideas, such as at the beginning of a case interview to synthesize your thoughts or when  brainstorming ideas in a structured way. To better understand why this tool is valuable, we have a deep dive into The Pyramid Principle .
• Hypothesis-Driven Approach : This is an approach to problem-solving where consultants begin by forming a hypothesis after understanding the client’s problem and high-level range of possibilities. Then, they gather data to test the initial hypothesis. If the data disproves the hypothesis, the consultants repeat the process with the next best hypothesis. To see more examples, read our article on how to apply a Hypothesis-Driven Approach .

– – – – – – –

In this article, we’ve covered:

• Understanding the purpose of a hypothesis tree
• What is different about a hypothesis tree vs. issue tree?
• How to build a hypothesis tree
• 4 tips on how to successfully use a hypothesis tree in your consulting case interview
• Other consulting concepts that are related to hypothesis trees

Still have questions?

If you have more questions about building a hypothesis tree, leave them in the comments below. One of My Consulting Offer’s case coaches will answer them.

Other people interested in the hypothesis tree found the following pages helpful:

• Our Ultimate Guide to Case Interview Prep
• Issue Trees
• Hypothesis-Driven Approach
• MECE Case Structure

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Design Thinking: The Scientific Method For Innovation

Insights - september 7, 2016.

When facing a challenging business problem or difficult strategic question, it can be hard to know where to start. In these situations, companies and organizations often turn to established strategies to create more value for their customers and improve their own positions in the market. For many companies, design thinking is a new and innovative method for solving problems and gaining new knowledge; for some, it is even considered “risky” because its popularity as a go-to process for creating innovative solutions is relatively new. But design thinking’s origins actually date back further than you might realize, pre-dating Aristotle. When you get down to it, design thinking is just the scientific method adapted for the purpose of creating of products, services, and experiences rooted in human experiences.

Discovery and hypothesis-based problem solving

Let’s go back to middle school for a moment, when we all probably first learned about the scientific method. In a nutshell, the scientific method emphasizes experimentation, discovery, and inductive reasoning. You start by making observations, often through the use of experiments, and combine the results of those experiments with existing facts. From these observations and experiments, you create informed hypotheses about how the natural world works. Then you test those hypotheses through additional experiments to see how accurate they are and if they can enter the realm of theory, law, and fact. If the observational data don’t support a hypothesis, you abandon it and explore what else may be supported by results. Overall, you seek to find new solutions by understanding what is already there.

“Science, at its core, is simply a method of practical logic that tests hypotheses against experience.” – John Michael Greer

Design thinking is the scientific method expanded to include observation and discovery of human behavior, the emotions behind those behaviors, and using that data to create innovative solutions to complex business problems. It can work really well in concert with the scientific method . Where the scientific method excels in understanding objective and quantitative data, design thinking offers a way to collect and understand subjective and qualitative data, such as customer wants, needs, as well as personal histories and experiences. These types of data are especially helpful in the earliest stages of a project when a lot may be unknown, even what problem you are trying to solve. It’s at this beginning stage that hypotheses are formed from the data and customer insights collected.  [ Read: The Robots Haven’t Won Yet (And Other Reasons I’m a Design Thinker) ]

Just like with the scientific method, you continuously test and validate (or invalidate) your hypotheses and ideas during a design thinking process. Instead of Petri dishes and pipettes in a lab, you may use “in the field” ethnographic observational tools such as a one-on-one interviews, fly-on–the-wall observations, and diary studies. Once you have a small collection of hypotheses validated based on a deep, inductive understanding your customer, you are ready to solve the right business problem.

Most professionals, particularly those in service industries, don’t rely on the scientific method in the way scientists have been trained to do. Design thinking can seem like a new and risky process to companies and organizations because they don’t recognize the similarities between design thinking and its well-established relative: the scientific method.

“The scientific method is nearly perfect for understanding the physical aspects of our life. But it is a radically limited viewfinder in its inability to offer values, morals, and meanings that are at the center of our lives.” – Huston Smith

Building a better fall jacket: Design thinking in action

The scientific method relies on testing a hypothesis within the parameters of the problem that the team is attempting to solve, and design thinking helps the team understand those parameters. By simulating the conditions in the desired context, the hypothesis can be either invalidated or supported, and new knowledge about the problem can be created. The parameters of the experiment simulate real world conditions as understood through design thinking, and make the results of the experiment more credible.

Maybe they assume the jacket should be waterproof for rainy days, and that it should be insulated for warmth. It should have plenty of pockets and have a detachable hood to keep the wearer’s head dry. They also assume that it should be reversible, durable, and colorful. They design a jacket that fits those parameters and conduct experiments that prove its capability, but when the jacket is released, it is widely panned as clunky and ugly. This approach fails because the team is hypothesizing with limited data and designing experiments based on unverified assumptions about what their customers desire. How could they discover what their customers actually want or need in a fall jacket?

By instead beginning the jacket design process with the principles of design thinking, the design team can create something that truly connects with their customers. Before hypothesizing or making assumptions about what jacket designs might sell, the design team begins with research to understand customer needs. They might conduct in-the-moment interviews with people shopping for jackets, observe people working outdoors in fall weather, and research emerging social trends. Through this process, the team is able to empathize with customers and can understand them as people rather than data points.

The design team also works to define their parameters. They discover, for example, that people buying fall jackets in the wet and temperate Pacific Northwest prioritize waterproofing and detachable hoods, whereas people in the Northeast prefer jackets with more insulation because their region is dryer and colder. The design team learns that, rather than a one-size-fits-all solution, there are market opportunities for several jacket designs. They also identify new customer needs that weren’t present when jackets of the past were designed: pockets have changed to accommodate what people carry with them today, including smart phones, e-readers, and tech accessories.

Through ideation and rapid prototyping, which is design thinking’s “experimentation,” the team can create educated hypotheses and test which concepts best meet the parameters established. The end result is a jacket designed for the needs of actual people based on data gathered through a design thinking-oriented process. Because they worked with actual customers and weren’t constrained by assumptions anchored in the past, the design team’s solution hypotheses are more meaningful and accurate.

Where the “design-tific” method works

Many businesses successfully use design thinking already. When Airbnb was struggling financially in 2009, the company used design thinking strategies to reconnect with their customers. They discovered that many of their listings weren’t catching the attention of potential guests because their owners had done a poor job photographing their spaces. They decided to step in and help the owners improve the quality and accuracy of their photos. They experimented with different strategies for how to represent their spaces until they found what worked. They applied the scientific method’s iterative, quantitative approaches along with design thinking’s human-focused discovery and found a solution to their problem that worked for everyone. Within a week, their customer-centric solution had doubled their revenue.

Humanitarian efforts have also benefited from combining the scientific method with design thinking. The Deworm the World Initiative used rigorous ideation and iteration to develop its strategy of increasing the quality of childhood education by combating parasitic worms. With the goal of improving the school attendance and test scores, DWI first tested several “obvious” solutions (additional textbooks, replacing textbooks with flipcharts, more teachers) before they discovered that treating worms in children had a much more significant impact, reducing absenteeism by 25% and raising incomes after leaving school by 20%. [note] 1. MaCaskill, W. (2015). Doing good better: How effective altruism can help you help others, do work that matters, and make smarter choices about giving back. New York: Avery[/note]  If DWI had not been open to learning from the failures of their earlier hypotheses, they would not have experimented with the techniques that eventually led them to solve the right problem and achieve success. By following the rigors of the scientific method and applying design thinking’s focus on the human experience, they were able to push beyond the obvious and find an actionable, if unexpected, solution.

By approaching a complex problem or question with a design-thinking-meets-scientific-method approach, companies and organizations can reliably and accurately serve their customers with the right products, services, and experiences.

Ready to bring the science of innovation to your workplace? Hire Mindhatch today!

You might also like....

• Design Thinking: A Key To Improving Organizational Culture
• How Human Resources Can Use Design Thinking to Improve Employee Engagement
• The Robots Haven’t Won Yet (And Other Reasons I’m a Design Thinker)

Coonoor Behal and Andrew Moore

Coonoor Behal is Founder and CEO of Mindhatch, and an experienced and recognized business strategy and innovation consultant with focused expertise in design thinking, improvisation, and innovation facilitation. Andrew Moore is a Design Strategist at Mindhatch and an expert in sustainable design.

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What is hypothesis-based consulting?

by Consultant's Mind | 11 comments

Hypothe – what?

Yes, I know it sounds like jargon , but actually it’s part of the secret sauce of management consulting .  It’s more than educated guessing; this is how consultants smartly break down complex or ambiguous problems, and quickly start driving towards an answer. At its heart is the scientific method – used for hundreds of years by scientists and thinkers to prove their ideas using evidence. Old school hat tip – Aristotle, Bacon, Descartes.

Hypotheses start early

For some, “hypothesis” is a word you last heard in science class. The concept is simple, but may seem a bit counter-intuitive when you put it into practice. In the generic project plan below, you can see that the hypothesis development happens early on. This typically looks like some best practices research, interviews with clients, and lots of whiteboard time. You put together some initial ideas ( logical starting points , not just wild guesses), quickly eliminate the bogus leads and focus on the promising ones. Like a wildcatter, you dig where there you think there will be oil. This is a mix of science, experience , and art .

Think broadly about the problem

Consultants have the time (clients have day-jobs) and the authority ( borrowed influence from their client executives) to cast a wide net for answers.

Often, the root causes of the problem sit elsewhere – in other functions, other business units, or even with suppliers. As groups get more specialized, they also get more silo-ed. Operational efficiency leads to enterprise-wide  sub-optimization .  Person A gets very efficient at her specific process, which creates downstream inefficiency for Person B somewhere else in the system.

In the example below, the client might believe ABC is the reason for the fall in market share, but in reality, it is a combination of other reasons that the client did not see (or want to admit). Let’s not mistake correlation with causation .

Treat hypotheses like suspects

Using the analogy of a TV detective from the 1970’s and 1980’s, Columbo would not rule out any suspects initially. He would survey the crime scene and start formulating some ideas on who the suspects were – based on eye-witness accounts, clues, and experience.  Keep sleuthing for clues until he was confident that suspect was either guilty or not guilty.

Same thing here. The goal is to put together a list of hypotheses (“suspects” using the crime analogy) that are distinct and separate . Then start going down the list to figure out if they are guilty or not. Divvy up and conquer the hypothesis list with your team .

This approach can be unnerving

Sometimes, clients find this uncomfortable because they inadvertently assume that the consultants comes to the project with the answers already . So, when the team spends the first few weeks interviewing people and gathering data , it can feel like the project is going slowly or sideways. Here are a few things clients can do:

• Help get the data that the consultants need to confirm / disprove the hypotheses
• Share previous project work which tried to solve the problem and failed
• Fast-track the ideas which you believe don’t need more (over-kill) evidence
• Do not be shy; ask what the key hypotheses are
• Bring in the right people (even if in other departments)

You get more confident over tmie

The consulting team’s confidence in the solution typically ebbs and flows during the project. As there is more fact-finding and discovery, new hypotheses are created and eventually whittled down. By the end of the project,  the team should be fairly confident in their answer and have the data and analysis to back-up their recommendations. As shown in the graphic below, there are lots of ups and downs , but confidence trends up.

Clients, give the consultants a little space

to take in the information and think deeply on the problem. A lot of the brain power is spent early in the project or during the proposal stage. Time well spent.

Oh Bill Gates. . .

In a famous story about Bill Gates, his mother was getting frustrated when he would not come to dinner or respond to her calls.  She demanded, “What are you doing?”

“ I am thinking, Mom.  Have you ever tried thinking? “ – Bill Gates

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11 Comments

So he gave all this money to charity to make up for being a prick to his mother!?!?!?!

Too funny. Naw, he was just being an average petulant pre-teenager, I am sure.

Basically it is the educated or calculated guess about some project success. Nice share though.

Really Good blog post.provided a helpful information .keep updating…

Many thanks for reading.

Encouraging — not to stop when you hit the low’s…

So true. So true. This graphic is my favorite depiction of the highs/lows of project-led life. . . https://www.pinterest.com/pin/195625177541414129/

Really nice and very well explained blog! You have covered all aspects meticulously yet briefly. Thanks for sharing!

Thank you for reading.

This reminds me of the “5 why” approach used for incident / accident investigation within the aviation domain.

If (A) is the the undesired outcome, so why did it happen?. Because of (B).

Why did (B) happen? Because of (C).

In most cases 5 iterations (hence 5 why) reveal the underlying root-cause.

Agree pretty strongly with that. Small nuance. 5 Why. asking questions. hypothesis, coming up with a statement which you can test and prove / disprove.

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Critical Thinking and Problem Solving toward Decision-Making

During the training the main critical thinking and problem solving techniques are introduced together with real-life examples. The difference between problem solving and decision making is examined and clarified.

Who is it for?

The course is suitable for business professionals interested in developing their critical thinking and learning how to better solve business problems.

Overview – why the topic is “critical” 

• Our changing VUCA world and why adaptability is key ▪ Key outcomes and what this means 
• Understanding where companies ‘stand’ and the  phase in which they are 
• Understanding how companies can grow – directions ▪ Understanding means & methods towards growth ▪ Understanding how to make decisions through SAF ▪ Understanding what areas need to be assessed during  SAF 
• Understanding what areas need to be assessed during  implementation 

Difference between Problem Solving & Decision  Making 

Black box thinking – technique & examples , root cause problem solving – technique and  examples , multi – criteria decision making .

• Breaking a company in 2: Outside & Inside ▪ What we control and what we don’t 
• A step by step approach (11 main areas) from outside  to inside  
• How to summarize and use the findings towards  Decision Making – Solving the “right problem” by  default 

Critical Thinking method 

• Systematic thinking 
• The “Mathematics” in finding solutions 
• Examples & activities 

Hypothesis based problem solving 

• Introduction to problem solving approaches 
• Introduction to hypothesis-based problem solving 
• Key takeaways

Dr. Constantine “Dino” Kiritsis 

International curriculum development expert, entrepreneur,  author, award winning training concept developer (hpd) .

Dino is an entrepreneur & consultant in the Business, HR, training & development industry. He is considered a world-class inspirational trainer/presenter having trained and led diverse events for numerous corporations and associations. He has delivered over 15,000 hours of professional training, hosting & presentations in the last 20 years in more than 40 countries in Europe, Asia and the Middle East mainly to corporate clients. 

He is also a consultant and International Curriculum Development expert for PwC’s Academy in the CEE and the Middle East. Dino has also done work with PwC’s Global Steering Committee for Private Company Services and has developed the award winning (Silver award, Boussias Education awards 2019) curriculum, methodology and mapping procedure for PwC’s Mini MBA programme being offered in the CEE region & the Middle East in more than 10 countries.

His knowledge areas span from Business Mapping, Business analysis, Entrepreneurship, Strategy and Corporate level training to developing programmes, career management and education, Professional qualifications (PQs) and teaching topics relating to Corporate & Business Strategy, Entrepreneurship, Business Planning, Innovation, Marketing and HR (for specialist qualifications (ACCA, CIA, CIMA, SHRM) and Universities on MBA and DBA programmes. 

He has been an active speaker on entrepreneurship, innovation, educational, professional training and business development issues in over 100 events and in the past decade. He holds a Bachelor’s degree from the University of Connecticut (USA), a Masters and a PhD from the University of Surrey (UK), a Diploma in Corporate Governance from the ACCA (Association of Chartered Certified Accountants) is an Associate Member (AICA) of the International Compliance Association and a Senior Certified Professional from the Society of Human Resource Management (SHRM – SMP) USA. He is a member of the board of SoFIA (School of the Future International Academy) in the UK and the President of the SHRM Global Forum for Greece and Cyprus.

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Hacking the Case Interview

An issue tree is a structured framework used to break down and analyze complex problems or questions into smaller components. It is a visual representation of the various aspects, sub-issues, and potential solutions related to a particular problem.

Issue trees are commonly used in business, consulting, problem-solving, and decision-making processes.

If you’re looking to better understand issue trees and how to use them in consulting case interviews or in business, we have you covered.

In this comprehensive article, we’ll cover:

• What is an issue tree?
• Why are issue trees important?
• How do I create an issue tree?
• How do I use issue trees in consulting case interviews?
• What are examples of issue trees?
• What are tips for making effective issue trees?

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course . These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

What is an Issue Tree?

An issue tree is a visual representation of a complex problem or question broken down into smaller, more manageable components. It consists of a top level issue, visualized as the root question, and sub-issues, visualized as branches and sub-branches.

• Top Level Issue (Root Question) : This is the main problem or question that needs to be addressed. It forms the root of the tree.
• Sub-issues (Branches) : Underneath the top level issue are branches representing the major categories or dimensions of the problem. These are the high-level areas that contribute to the overall problem.
• Further Sub-issues (Sub-branches) : Each branch can be broken down further into more specific sub-issues.

Issue trees generally take on the following structure.

Issue trees get their name because the primary issue that you are solving for can be broken down into smaller issues or branches. These issues can then be further broken down into even smaller issues or branches.

This can be continued until you are left with a long list of small issues that are much simpler and more manageable. No matter how complicated or difficult a problem is, an issue tree can provide a way to structure the problem to make it easier to solve.

As an example, let’s say that we are trying to help a lemonade stand increase their profits. The overall problem is determining how to increase profits.

Since profits is equal to revenue minus costs, we can break this problem down into two smaller problems:

• How can we increase revenues?
• How can we decrease costs?

Since revenue is equal to quantity times price, we can further break this revenue problem down into two even smaller problems:

• How can we increase quantity sold?
• How can we increase price?

Looking at the problem of how to increase quantity sold, we can further break that problem down:

• How can we increase the quantity of lemonade sold?
• How can we increase the quantity of other goods sold?

We can repeat the same procedure for the costs problem since we know that costs equal variable costs plus fixed costs.

• How can we decrease variable costs?
• How can we decrease fixed costs?

Looking at the problem of how to decrease variable costs, we can further break that down by the different variable cost components of lemonade:

• How can we decrease costs of lemons?
• How can we decrease costs of water?
• How can we decrease costs of ice?
• How can we decrease costs of sugar?
• How can we decrease costs of cups?

The overall issue tree for this example would look like the following:

In this example, the issue tree is a special kind of issue tree known as a profit tree.

Why are Issue Trees Important?

Issue trees are helpful because they facilitate systematic analysis, managing complexity, prioritization, generating solutions, identifying root causes, work subdivision, roadmap generation, and effective communication.

Systematic analysis : Issue trees guide a systematic analysis of the problem. By dissecting the problem into its constituent parts, you can thoroughly examine each aspect and understand its implications.

Managing complexity : Complex problems often involve multiple interrelated factors. Issue trees provide a way to manage this complexity by organizing and visualizing the relationships between different components.

Prioritization : Issue trees help in prioritizing actions. By assessing the importance and impact of each sub-issue, you can determine which aspects of the problem require immediate attention.

Generating solutions : Issue trees facilitate the generation of potential solutions or strategies for each component of the problem. This allows for a more comprehensive approach to problem-solving.

Identifying root causes : Issue trees help in identifying the root causes of a problem. By drilling down through the sub-issues, you can uncover the underlying factors contributing to the main issue.

Work subdivision : Issue trees provide you with a list of smaller, distinct problems or areas to explore. This distinction makes it easy for you to divide up work.

Roadmap generation : Issue trees layout exactly all of the different areas or issues that you need to focus on in order to solve the overall problem. This gives you a clear idea of where to focus your attention and work on.

Effective communication : Issue trees are powerful communication tools. Visualizing the problem in a structured format helps in explaining it to others, including team members, stakeholders, or clients.

How Do I Create An Issue Tree?

Creating an issue tree involves several steps. Here's a step-by-step guide to help you through the process:

Step 1: Define the top-level issue

Start by clearly articulating the main problem or question that you want to address. This will form the root of your issue tree.

Step 2: Identify the branches (sub-issues)

Consider the major sub-issues that contribute to the overall problem. These will become the branches of your issue tree. Brainstorm and list them down.

There are four major ways that you can break down the root problem in an issue tree. You can break down the issue by stakeholder, process, segments, or math.

• Stakeholder : Break the problem down by identifying all stakeholders involved. This may include the company, customers, competitors, suppliers, manufacturers, distributors, and retailers. Each stakeholder becomes a branch for the top-level issue.
• Process : Break the problem down by identifying all of the different steps in the process. Each step becomes a branch for the top-level issue.
• Segment : Break the problem down into smaller segments. This may include breaking down the problem by geography, product, customer segment, market segment, distribution channel, or time horizon. Each segment becomes a branch for the top-level issue.
• Math : Break a problem down by quantifying the problem into an equation or formula . Each term in the equation is a branch for the top-level issue.

Step 3: Break down each branch

For each branch, ask yourself if there are further components that contribute to it. If so, break down each branch into more specific components. Continue this process until you've reached a level of detail that allows for meaningful analysis.

Similar to the previous step, you can break down a branch by stakeholder, process, segment, or by math.

Step 4: Review and refine

Take a step back and review your issue tree. Make sure it accurately represents the problem and its components. Look for any missing or redundant branches or sub-issues.

Step 5: Prioritize and evaluate

Consider assigning priorities to different sub-issues or potential solutions. This will help guide your decision-making process.

How Do I Use Issue Trees in Consulting Case Interviews?

Issue trees are used near the beginning of the consulting case interview to break down the business problem into smaller, more manageable components.

After the interviewer provides the case background information, you’ll be expected to quickly summarize the context of the case and verify the case objective. After asking clarifying questions, you’ll ask for a few minutes of silence to create an issue tree.

After you have created an issue tree, here’s how you would use it:

Step 1: Walk your interviewer through the issue tree

Once you’ve created an issue tree, provide a concise summary of how it's structured and how it addresses the problem at hand. Explain the different branches and sub-branches. They may ask a few follow-up questions.

As you are presenting your issue tree, periodically check in with the interviewer to ensure you're on the right track. Your interviewer may provide some input or guidance on improving your issue tree.

Step 2: Identify an area of your issue tree to start investigating

Afterwards, you’ll use the issue tree to help identify a branch to start investigating. There is generally no wrong answer here as long as you have a reason that supports why you want to start with a particular branch.

To determine which branch to start investigating, ask yourself a few questions. What is the most important sub-issue? Consider factors like urgency, impact, or feasibility. What is your best guess for how the business problem can be solved?

Step 3: Gather data and information

Collect relevant facts, data, and information for the sub-issue that you are investigating. This will provide the necessary context and evidence for your analysis.

Step 4 : Record key insights on the issue tree

After diving deeper into each sub-issue or branch on your issue tree, you may find it helpful to write a few bullets on the key takeaways or insights that you’ve gathered through your analysis.

This will help you remember all the work that you have done during the case interview so far. It’ll also help you develop a recommendation at the end of the case interview because you’ll quickly be able to read a summary of all of your analysis.

Step 5: Iterate and adjust as needed

As you work through the problem-solving process, be prepared to adjust and update the issue tree based on new information, insights, or changes in the situation.

Remember, creating an issue tree is not a one-size-fits-all process. It's a dynamic tool that can be adapted to suit the specific needs and complexity of the problem you're addressing.

Step 6: Select the next area of your issue tree to investigate

Once you have finished analyzing a branch or sub-issue on your issue tree and reached a satisfactory insight or conclusion, move onto the next branch or sub-issue.

Again, consider factors like urgency, impact, or feasibility when prioritizing which branch or sub-issue to dive deeper into. Repeat this step until the end of the case interview when you are asked for a final recommendation.

What are Examples of Issue Trees?

Below are five issue tree examples for five common types of business situations and case interviews.

If you want to learn strategies on how to create unique and tailored issue trees for any case interview, check out our comprehensive article on case interview frameworks .

Profitability Issue Tree Example

Profitability cases ask you to identify what is causing a company’s decline in profits and what can be done to address this problem.

A potential issue tree template for this case could explore four major issues:

• What is causing the decline in profitability?
• Is the decline due to changes among customers?
• Is the decline due to changes among competitors?
• Is the decline due to market trends?

Market Entry Issue Tree Example

Market entry cases ask you to determine whether a company should enter a new market.

• Is the market attractive?
• Are competitors strong?
• Does the company have the capabilities to enter?
• Will the company be profitable from entering the market?

Merger and Acquisition Issue Tree Example

Merger and acquisition cases ask you to determine whether a company or private equity firm should acquire a particular company.

• Is the market that the target is in attractive?
• Is the acquisition target an attractive company?
• Are there any acquisition synergies?
• Will the acquisition lead to high returns?

New Product Issue Tree Example

New product cases ask you to determine whether a company should launch a new product or service.

• Will customers like the product?
• Does the company have the capabilities to successfully launch the product?
• Will the company be profitable from launching the product?

Pricing Issue Tree Example

Pricing cases ask you to determine how to price a particular product or service.

A potential issue tree template for this case could explore three major issues:

• How should we price based on the product cost?
• How should we price based on competitors’ products?
• How should we price based on customer value?

What are Tips for Making Effective Issue Trees?

Issue trees are powerful tools to solve complex business problems, but they are much less effective if they don’t follow these important tips.

Issue tree tip #1: Be MECE

MECE stands for mutually exclusive and collectively exhaustive. When breaking down the overall problem in your issue tree, the final list of smaller problems needs to be mutually exclusive and collectively exhaustive.

Mutually exclusive means that none of the smaller problems in your issue tree overlap with each other. This ensures that you are working efficiently since there will be no duplicated or repeated work.

For example, let’s say that two of the issues in your issue tree are:

• Determine how to increase cups of lemonade sold
• Determine how to partner with local organizations to sell lemonade

This is not mutually exclusive because determining how to partner with local organizations would include determining how to increase cups of lemonade sold.

In determining how to increase cups of lemonade sold, you may be duplicating work from determining how to partner with local organizations.

Collectively exhaustive means that the list of smaller problems in your issue tree account for all possible ideas and possibilities. This ensures that your issue tree is not missing any critical areas to explore.

For example, let’s say that you break down the issue of determining how to decrease variable costs into the following issues:

This is not collectively exhaustive because you are missing two key variable costs: sugar and cups. These could be important areas that could increase profitability, which are not captured by your issue tree.

You can read a full explanation of this in our article on the MECE principle .

Issue tree tip #2: Be 80/20

The 80/20 principle states that 80% of the results come from 20% of the effort or time invested.

In other words, it is a much more efficient use of time to spend a day solving 80% of a problem and then moving onto solving the next few problems than to spend five days solving 100% of one problem.

This same principle should be applied to your issue tree. You do not need to solve every single issue that you have identified. Instead, focus on solving the issues that have the greatest impact and require the least amount of work.

Let’s return to our lemonade stand example. If we are focusing on the issue of how to decrease costs, we can consider fixed costs and variable costs.

It may be a better use of time to focus on decreasing variable costs because they are generally easier to lower than fixed costs.

Fixed costs, such as paying for a business permit or purchasing a table and display sign, typically have long purchasing periods, making them more difficult to reduce in the short-term.

Issue tree tip #3: Have three to five branches

Your issue tree needs to be both comprehensive, but also clear and easy to follow. Therefore, your issue tree should have at least three branches to be able to cover enough breadth of the key issue.

Additionally, your issue tree should have no more than five branches. Any more than this will make your issue tree too complicated and difficult to follow. By having more than five branches, you also increase the likelihood that there will be redundancies or overlap among your branches, which is not ideal.

Having three to five branches helps achieve a balance between going deep into specific sub-issues and covering a broad range of aspects. It balances breadth and depth.

Issue tree tip #4: Clearly define the top-level issue

Make sure that you clearly articulate the main problem or question. This sets the foundation for the entire issue tree. If you are addressing the wrong problem or question, your entire issue tree will be useless to you.

Issue tree tip #5: Visualize the issue tree clearly

If you're using a visual representation, make sure it's easy to follow. Use clean lines, appropriate spacing, and clear connections between components.

Keep your issue tree organized and neat. A cluttered or disorganized tree can be confusing and difficult to follow.

Ensure that each branch and sub-issue is labeled clearly and concisely. Use language that is easily understandable to your audience.

Issue tree tip #6: Order your branches logically

Whenever possible, try to organize the branches in your issue tree logically.

For example, if the branches in your issue tree are segmented by time, arrange them as short-term, medium-term, and long-term. This is a logical order that is arranged by length of time.

It does not make sense to order the branches as long-term, short-term, and medium- term. This ordering is confusing and will make the entire issue tree harder to follow.

Issue tree tip #7: Branches should be parallel

The branches on your issue tree should all be on the same logical level.

For example, if you decide to segment the branches on your issue tree by geography, your branches could be: North America, South America, Europe, Asia, Africa, and Australia. This segmentation is logical because each segment is a continent.

It would not make sense to segment the branches on your issue as United States, South America, China, India, Australia, and rest of the world. This segmentation does not follow logical consistency because it mixes continents and countries.

Issue tree tip #8: Practice and get feedback

It takes practice to create comprehensive, clear, and concise issue trees. This is a skill that takes time to develop and refine.

When you initially create your first few issue trees, it may take you a long period of time and you may be missing key sub-issues. However, with enough practice, you’ll be able to create issue trees effortlessly and effectively.

Practice creating issue trees on different problems to improve your skills. Seek feedback from peers or mentors to refine your approach.

Recommended Case Interview Resources

Here are the resources we recommend to learn the most robust, effective case interview strategies in the least time-consuming way:

• Comprehensive Case Interview Course (our #1 recommendation): The only resource you need. Whether you have no business background, rusty math skills, or are short on time, this step-by-step course will transform you into a top 1% caser that lands multiple consulting offers.
• Hacking the Case Interview Book   (available on Amazon): Perfect for beginners that are short on time. Transform yourself from a stressed-out case interview newbie to a confident intermediate in under a week. Some readers finish this book in a day and can already tackle tough cases.
• The Ultimate Case Interview Workbook (available on Amazon): Perfect for intermediates struggling with frameworks, case math, or generating business insights. No need to find a case partner – these drills, practice problems, and full-length cases can all be done by yourself.
• Case Interview Coaching : Personalized, one-on-one coaching with former consulting interviewers
• Behavioral & Fit Interview Course : Be prepared for 98% of behavioral and fit questions in just a few hours. We'll teach you exactly how to draft answers that will impress your interviewer
• Resume Review & Editing : Transform your resume into one that will get you multiple interviews

Land Multiple Consulting Offers

Complete, step-by-step case interview course. 30,000+ happy customers.

The Genius Blog

Hypothesis Testing Solved Examples(Questions and Solutions)

Here is a list hypothesis testing exercises and solutions. Try to solve a question by yourself first before you look at the solution.

Question 1 In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication  has a mean of 140. Did the medication affect intelligence? View Solution to Question 1

A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get the following scores:62, 92, 75, 68, 83, 95. Can the professor have 90% confidence that the mean score for the class on the test would be above 70. Solution to Question 2

Question 3 In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine would pack faster on the average than the machine currently used. To test the hypothesis, the time it takes each machine to pack ten cartons are recorded. The result in seconds is as follows.

Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform  the required hypothesis test at the 5% level of significance. Solution to Question 3 

Question 4 We want to compare the heights in inches of two groups of individuals. Here are the measurements: X: 175, 168, 168, 190, 156, 181, 182, 175, 174, 179 Y:  120, 180, 125, 188, 130, 190, 110, 185, 112, 188 Solution to Question 4 

Question 5 A clinic provides a program to help their clients lose weight and asks a consumer agency to investigate the effectiveness of the program. The agency takes a sample of 15 people, weighing each person in the sample before the program begins and 3 months later. The results a tabulated below

Determine is the program is effective. Solution to Question 5

Question 6 A sample of 20 students were selected and given a diagnostic module prior to studying for a test. And then they were given the test again after completing the module. . The result of the students scores in the test before and after the test is tabulated below.

We want to see if there is significant improvement in the student’s performance due to this teaching method Solution to Question 6 

Question 7 A study was performed to test wether cars get better mileage on premium gas than on regular gas. Each of 10 cars was first filled with regular or premium gas, decided by a coin toss, and the mileage for the tank was recorded. The mileage was recorded again for the same cars using other kind of gasoline. Determine wether cars get significantly better mileage with premium gas.

Mileage with regular gas: 16,20,21,22,23,22,27,25,27,28 Mileage with premium gas: 19, 22,24,24,25,25,26,26,28,32 Solution to Question 7 

Question 8  An automatic cutter machine must cut steel strips of 1200 mm length. From a preliminary data, we checked that the lengths of the pieces produced by the machine can be considered as normal random variables  with a 3mm standard deviation. We want to make sure that the machine is set correctly. Therefore 16 pieces of the products are randomly selected and weight. The figures were in mm: 1193,1196,1198,1195,1198,1199,1204,1193,1203,1201,1196,1200,1191,1196,1198,1191 Examine wether there is any significant deviation from the required size Solution to Question 8

Question 9 Blood pressure reading of ten patients before and after medication for reducing the blood pressure are as follows

Patient: 1,2,3,4,5,6,7,8,9,10 Before treatment: 86,84,78,90,92,77,89,90,90,86 After treatment:    80,80,92,79,92,82,88,89,92,83

Test the null hypothesis of no effect agains the alternate hypothesis that medication is effective. Execute it with Wilcoxon test Solution to Question 9

Question on ANOVA Sussan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides 24 students into three groups of 8 each. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with nose that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores are tabulated below.

Group1: Constant sound: 7,4,6,8,6,6,2,9 Group 2: Random sound: 5,5,3,4,4,7,2,2 Group 3: No sound at all: 2,4,7,1,2,1,5,5 Solution to Question 10

Question 11 Using the following three groups of data, perform a one-way analysis of variance using α  = 0.05.

Solution to Question 11

Question 12 In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine would pack faster on the average than the machine currently used. To test the hypothesis, the time it takes each machine to pack ten cartons are recorded. The result in seconds is as follows.

New Machine: 42,41,41.3,41.8,42.4,42.8,43.2,42.3,41.8,42.7 Old Machine:  42.7,43.6,43.8,43.3,42.5,43.5,43.1,41.7,44,44.1

Perform an F-test to determine if the null hypothesis should be accepted. Solution to Question 12

Question 13 A random sample 500 U.S adults are questioned about their political affiliation and opinion on a tax reform bill. We need to test if the political affiliation and their opinon on a tax reform bill are dependent, at 5% level of significance. The observed contingency table is given below.

Solution to Question 13

Question 14 Can a dice be considered regular which is showing the following frequency distribution during 1000 throws?

Solution to Question 14

Solution to Question 15

Question 16 A newly developed muesli contains five types of seeds (A, B, C, D and E). The percentage of which is 35%, 25%, 20%, 10% and 10% according to the product information. In a randomly selected muesli, the following volume distribution was found.

Lets us decide about the null hypothesis whether the composition of the sample corresponds to the distribution indicated on the packaging at alpha = 0.1 significance level. Solution to Question 16

Question 17 A research team investigated whether there was any significant correlation between the severity of a certain disease runoff and the age of the patients. During the study, data for n = 200 patients were collected and grouped according to the severity of the disease and the age of the patient. The table below shows the result

Let us decided about the correlation between the age of the patients and the severity of disease progression. Solution to Question 17

Question 18 A publisher is interested in determine which of three book cover is most attractive. He interviews 400 people in each of the three states (California, Illinois and New York), and asks each person which of the  cover he or she prefers. The number of preference for each cover is as follows:

Do these data indicate that there are regional differences in people’s preferences concerning these covers? Use the 0.05 level of significance. Solution to Question 18

Question 19 Trees planted along the road were checked for which ones are healthy(H) or diseased (D) and the following arrangement of the trees were obtained:

H H H H D D D H H H H H H H D D H H D D D

Test at the    = 0.05 significance wether this arrangement may be regarded as random

Solution to Question 19 

Question 20 Suppose we flip a coin n = 15 times and come up with the following arrangements

H T T T H H T T T T H H T H H

(H = head, T = tail)

Test at the alpha = 0.05 significance level whether this arrangement may be regarded as random.

Solution to Question 20

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Below are given the gain in weights (in lbs.) of pigs fed on two diet A and B Dieta 25 32 30 34 24 14 32 24 30 31 35 25 – – DietB 44 34 22 10 47 31 40 30 32 35 18 21 35 29