Question

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If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 16. The superintendent wants to know if there is a disparity in teaching quality, and decides to investigate whether the standard deviation of test scores has changed. She samples 26 random students and finds a mean score of 186 with a standard deviation of 7.276. Is there evidence that the standard deviation of test scores has decreased at the α=0.005 level? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

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 to three decimal places.

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

Step 4 of 5: Make the decision Reject Null Hypothesis OR Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion? There is sufficient evidence to show that the standard deviation of the test scores has decreased OR There is not sufficient evidence to show that the standard deviation of the test scores has decreased.

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Answer #1

The statistical software output for this problem is:

Hence,

Step - 1: Hypotheses:

Step - 2: Critical value = 10.520

Step - 3: Test statistic = 5.170

Step - 4: Reject the null hypothesis

Step - 5: There is sufficient evidence to show that the standard deviation of the test scores has decreased.

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