Refer to Exercise 22. There a study examined the average hospital stay for patients under the care of each of two classes of physicians— hospitalists and general internists. Suppose now that the two population standard deviations are unknown and that sample results were as follows: Patients in the sample who were cared for by internists stayed for an average of 4.59 days, with a sample standard deviation of 1.8 days, while patients in the sample who were cared for by hospitalists had an average stay of 4.1 days, with a sample standard deviation of 1.3 days. Set up the appropriate hypothesis test to test a “no difference in population means” null hypothesis at the 1% significance level, assuming sample sizes were
a. 10 patients who were cared for by internists and 15 patients who were cared for by hospitalists. Assume that the population distributions are normal and have equal standard deviations.
b. 100 patients who were cared for by internists and 150 patients who were cared for by hospitalists.