Question

If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 27 . 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 161 with a standard deviation of 13.2914 . Is there evidence that the standard deviation of test scores has decreased at the α = 0.01 level?

Assume the population is normally distributed. 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.

Answer 1

Let be the population standard deviation .

We want to test whether is changed from 27

So our Hypotheses are

Ho : = 27 vs Ha :

From sample, sample size n= 25

Sample standard deviation s = 13.2914

Test statictic is

= 5.816

Here alpha = 0.01 and df for chi square distribution is n-1 = 24

This is two tailed test . From chi square table

Upper critical value = 45.558

Lower critical value = 9.886

We will Reject Ho if test statistic is less than 9.886 or more than 45.558

Here test statistic is less than 9.886

So reject Ho

There is enough evidence that standard deviation has changed and also standard deviation has decreased.