Question

The following data are scores on a standardized statistics examination for independent random samples of students from two small liberal arts colleges.

College A: 78, 84, 81, 78, 76, 83, 79, 75, 85, 81 College B: 89, 78, 83, 85, 87, 78, 85, 94, 88, 87

Calculate the sample variance (or standard deviation) for each college.

For the test of homogeneity,

Ho: σ²A = σ²B Ha: σ²A ≠ σ²B

calculate the test statistic F'.

For α = 0.05, specify the critical region for the test of homogeneity and make a decision about H_o.

Find the P-value and compare to α = 0.05.

Answer 1

Answer:-

F critical = F_{​​​​​9,9,0.05/2} = 4.03 ( for two sided region)

Reference

Decision :- F < F critical , So we may accept Ho.

Conclusion :- College A and College B has homogeneous variance

P-value at alpha = 0.05 and F = 2.102

P-value = 0.284

Conclusion :- P-value > alpha , so we may accept Ho.

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Thanks dear student