In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of
scores from all of the students who took the test. She sees that the mean score is
with a standard deviation of
. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was
10. Is there evidence that the standard deviation of test scores has decreased at the α = 0.025 level? Assume the population is normally distributed.
State the null and alternative hypotheses. Round to four decimal places when necessary.
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.
Determine the value of the test statistic. Round your answer to three decimal places.
Make the decision.
What is the conclusion?
There is sufficient evidence to show that the standard deviation of the test scores has decreased.
There is not sufficient evidence to show that the standard deviation of the test scores has decreased.