hypothesis test about standard deviation

A test of a single standard deviation assumes that the underlying distribution is normal. The null and alternative hypotheses are stated in terms of the population standard deviation (or population variance). The test statistic is: χ2 = (n − 1)s2 σ2 (8.4.1) (8.4.1) χ 2 = ( n − 1) s 2 σ 2. where:

Performing a Hypothesis Test Regarding σ. Step 1: State the null and alternative hypotheses. Step 2: Decide on a level of significance, α. Step 3: Compute the test statistic, . Step 4: Determine the P -value. Step 5: Reject the null hypothesis if the P -value is less than the level of significance, α.

This is a test on a population mean where the population standard deviation is unknown (we only know the sample standard deviation [latex]s=1.8.[/latex]). So we use a [latex]t[/latex]-distribution to calculate the p-value. Because the alternative hypothesis is a [latex]\lt[/latex], the p-value is the area in the left-tail of the distribution.

The alternative hypothesis is that the true population standard deviation is not equal to 3.25 . We want to test the null hypothesis, H0: σ = 3.25 , against the alternative hypothesis, H1: σ ≠ 3.25 , at the 0.0333 level of significance . Note that this is a two-tailed test .

Use the form of the alternative hypothesis to determine if the test is left-tailed, right-tailed, or two-tailed. Collect the sample information for the test and identify the significance level. When the population standard deviation is known, find the p-value (the area in the corresponding tail) for the test using the normal distribution.

Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings. Other interesting articles. Frequently asked questions about hypothesis testing.

In this section you will conduct hypothesis tests on single means when the population standard deviation is known. Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will perform some variation of these steps: Define hypotheses.

Population standard deviation is known. As I mention in the Z test vs T test section, use a Z test when you know the population standard deviation. However, when n > 30, the difference between the analyses becomes trivial. Related post: Standard Deviations. Z Test Formula. These Z test formulas allow you to calculate the test statistic.

What test can be used to determine if two samples have similar variances? What causes the null hypothesis to be rejected in an F-test? View all chapters. The best videos and questions to learn about Hypothesis Testing for the Standard Deviation. Get smarter on Socratic.

where: n = the total number of data ; s 2 = sample variance ; σ 2 = population variance; You may think of s as the random variable in this test. The number of degrees of freedom is df = n - 1.A test of a single variance may be right-tailed, left-tailed, or two-tailed. Example 11.10 will show you how to set up the null and alternative hypotheses. The null and alternative hypotheses contain ...

A test statistic assesses how consistent your sample data are with the null hypothesis in a hypothesis test. Test statistic calculations take your sample data and boil them down to a single number that quantifies how much your sample diverges from the null hypothesis. As a test statistic value becomes more extreme, it indicates larger ...

A test of a single variance assumes that the underlying distribution is normal.The null and alternative hypotheses are stated in terms of the population variance (or population standard deviation). The test statistic is: [latex]\displaystyle\dfrac{\left(n-1\right)s^2}{\sigma^2}[/latex]

Assumptions. When you perform a hypothesis test of a single population mean μ using a normal distribution (often called a z-test), you take a simple random sample from the population. The population you are testing is normally distributed, or your sample size is sufficiently large.You know the value of the population standard deviation, which, in reality, is rarely known.

How to conduct a hypothesis test for a mean value, using a one-sample t-test. The test procedure is illustrated with examples for one- and two-tailed tests. ... where s is the standard deviation of the sample, N is the population size, and n is the sample size. When the population size is much larger (at least 20 times larger) than the sample ...

Example problem: A sample of 200 people has a mean age of 21 with a population standard deviation (σ) of 5. Test the hypothesis that the population mean is 18.9 at α = 0.05. Step 1: State the null hypothesis. In this case, the null hypothesis is that the population mean is 18.9, so we write: H 0: μ = 18.9. Step 2: State the alternative ...

The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: \(H_{0}: \bar{x} = 4.5, H_{a}: \bar{x} > 4.5\) ... From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires ...

College A sampled 11 graduates. Their average is four math classes with a standard deviation of 1.5 math classes. College B sampled nine graduates. Their average is 3.5 math classes with a standard deviation of one math class. The community group believes that a student who graduates from college A has taken more math classes, on average.