Two universities (A and B) require first year applicants to write the same standardized entrance exam. The data below give the exam scores of independent random samples of applicants from each of these schools.
UniversityA 91 76 71 76 76 88 84 73 63 72 75 81 77 68 65 67 79 72 83 72 79 68 69
UniversityB 60 57 53 68 57 90 35 54 56 64 57 47 62 45 74 70 66 78 64 66 85 41
Assume the samples come from normal distributions.
(a) Determine which procedure, the two sample pooled t-test or unpooled t-test, is more appropriate for this data.
(b) Use the procedure selected in (a) to determine if, on average, the exam scores of applicants to university A are higher than those of applicants to university B. (a = .05)
(c) Construct a 99% confidence interval for the mean difference of exam scores between the two universities.