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.
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
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.
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