Question

A standardized test is given to an eighth grade class and a seventh grade class. The superintendent believes that the variance in performance from the eighth grade class is greater than the variance in performance from the seventh grade class. The sample variance of a sample of 19 test scores from the eighth grade class is 29.94. The sample variance of a sample of 19 test scores from the seventh grade class is 20.2. Test the claim using a 0.025 level of significance. Let σ21 represent the population variance for eighth grade class.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer(s) to four decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to four decimal places.

Step 4 of 5: Make a decision.

Step 5 of 5: State the test's conclusion. Does the evidence support the claim?

Answer 1

To test :

Test statistic :

We reject the null hypothesis or H₀ if the observed value of , where ,

Critical value :

Test statistic :

Now ,

Hence we accept the null hypothesis or H₀ .

Thus we do not have sufficient evidence to support the claim that the variance in performance from the eighth grade class is greater than the variance in performance from the seventh grade class.