If the quality of teaching is similar in a school, the scores on
a standardized test will have a standard deviation of
12. 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
25 random students and finds a mean score of
156 with a standard deviation
of 5.4822. Is there evidence that the
standard deviation of test scores has decreased at the
α=0.1 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.