Question

A standardized test is given to an eighth grade class and an eleventh grade class. The superintendent believes that the variance in performance from the eighth grade class is smaller than the variance in performance from the eleventh grade class. The sample variance of a sample of 4 test scores from the eighth grade class is 22.72. The sample variance of a sample of 14 test scores from the eleventh grade class is 26.36. Test the claim using a 0.025 level of significance. Let σ21 represent the population variance for eighth grade class.

Step 3 of 5 : Compute the value of the test statistic. Round your answer to four decimal places. Answer

Answer 1

Given,

We have to test the below hypotheses at α=0.025

H₀: vs. H₁:

The test statistic to test the above hypotheses is F test with (n₁ -1, n₂ -1)df

The value of Test statistic = 0.8619

The critical value of a left tailed F test at α=0.025 with (3,13)df is

F_(0.025,3,13) = 0.0699

Here we have left tailed F critical is less than F calculated which indicates that we do not have enough evidence against H₀ to reject it so we fail to reject H₀.

On the basis of above results and evidences, we can conclude that the belief of superintendent is not true.