Question

A professor takes a random sample of 25 students and administers a test with questions increasing in difficulty. He takes another sample of 25 students and administers a test with questions decreasing in difficulty. He records measures of test anxiety based on a scale from 1 to 10 (most anxious). Using steps below, run an F test to test the claim that the two given samples come from populations with different variances. Use α = 0.01.

Questions with Increasing Difficulty	Questions with Decreasing Difficulty
3.7	4.8
4.5	6.2
2.9	5.9
1.7	5.1
4.5	7.8
6.2	9.5
3.8	6.3
2.9	8.5
1.7	8.0
4.2	6.8
4.7	6.4
3.8	4.9
3.1	5.6
3.0	8.8
1.7	9.4
2.0	9.5
1.4	6.5
2.4	7.6
1.6	6.7
5.6	8.2
6.7	5.6
5.4	4.2
3.6	7.9
2.4	8.1
3.7	6.5

A. State the null and alternative hypotheses in terms of σ₁² & σ₂². Be sure to label which population is which.

B. Find the critical value, Test statistic, and P-value

C. Decision? Reject / Fail to Reject

D. Are the two given samples from populations with different variances? yes/no

Answer 1