A standardized test is given to a sixth grade class. Historically, the test scores have had a standard deviation of 11. The superintendent believes that the standard deviation of performance may have recently changed. She randomly sampled 21 students and found a mean of 180 with a standard deviation of 5.769. Is there evidence that the standard deviation of test scores has decreased at the =0.05 level? Assume the population is normally distributed.

1)State the null and alternative hypotheses. Round to four decimal places when necessary.

2)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.

3)Determine the value of the test statistic. Round your answer to three decimal places.

4)Make the decision.

5)What is the conclusion?