Question

22. A study conducted at the University of Chicago Hospitals compared the hospital-related perfor- mance of “hospitalists”—physicians specializing in caring for hospitalized patients—to the performance of general internists who devote only a small percent- age of their time caring for hospitalized patients. One of the variables examined was the average time that patients under the care of each of these two classes of physicians spent in the hospital. Patients in the sample who were cared for by internists stayed for an average of 4.59 days, while patients in the sample who were cared for by hospitalists left after an aver- age stay of 4.1 days (source: uchospitals.edu). Construct a hypothesis test to test the null hypoth- esis that there would be no difference in the average hospital stay for the two populations represented here. Use a significance level of 1%. Assume the sam- ple sizes were 488 for the internist patient sample and 162 for the hospitalist patient sample. Also assume that the population standard deviations are known: 1.5 days for the internist patient population and 1.4 days for the hospitalist patient populatio

Answer 1

US + n2 2 ☺ 3.7907 TI Ang let Midl2 be the population average time that patients undes the care of internists and by hospitalists respectively. Then given that for ni= 480, X,= 4.59 days, o = 1.5 for n2 = 162, X2 = 4.1 days, 0,= 1.4 The hull and alternative hypotheses are Hoi Mi = M2 Ha! Mi #M2 XI-X The test statistis is za ~ N(oll under Ho 0,2 02 4.59 - 4.1 0.49 (1.512 0.129265 408 162 The p-value is p-value = P(Z <-3.7907) + P(273.7 907) = 2(1-3 (3.7907)) = 211- 0.999925) 0.00015 since p-value in less than level of significance d=0,01, 10 we reglect Ho at 2=0.01: So we conclude that there is insufficient evidence to support the hull hypothesis that there would be no difference in average hospital stay for the two population. +(1.4)