Independent random samples of patients who had received knee and hip replacement were asked to assess the quality of service on a scale from 1 (low) to 7 (high). For a sample of 83 knee patients, the...

Independent random samples of patients who had received knee and hip replacement were asked to assess the quality of service on a scale from 1 (low) to 7 (high). For a sample of 83 knee patients, the mean rating was 6.543 and the sample standard deviation was 0.649. For a sample of 54 hip patients, the mean rating was 6.733 and the sample standard deviation was 0.425. Test, against a two-sided alternative, the null hypothesis that the population mean ratings for these two types of patients are the same. Of a random sample of 148 accounting majors, 75 rated a sense of humor as a very important trait to their career performance. This same view was held by 81 of an independent random sample of 178 finance majors.

a. Test, at the 5% level, the null hypothesis that at least one-half of all finance majors rate a sense of humor as very important.

b. Test, at the 5% level against a two-sided alternative, the null hypothesis that the population proportions of accounting and finance majors who rate a sense of humor as very important are the same.