Question

If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 15. 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 152 with a standard deviation of 5.7079. Is there evidence that the standard deviation of test scores has decreased at the α=0.025 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.

Answer 1

Given, s = 5.7079 so s² = 5.7079*5.7079 = 32.5801224

Hypothesized Standard Deviation = 15, so Hypothesized variance = 15*15 = 225

Based on the information provided, the significance level is α=0.025 and df = 26-1 = 25.

The critical χ² value = 13.120

Test statistic χ² = 3.619

At 0.025 significance level, there is enough evidence to claim that the standard deviation of test scores has decreased.