In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 prostatectomy patients, while in Paymor Hospital such exams were given in 110 out of 200 cases. In a left-tailed test for equality of proportions, the p-value is:
A).9772
B).0228
C).4772
D).0517

Question

Quizplus · Accepted Answer

We can use a two-sample z-test for proportions. The null hypothesis is that the proportion of patients receiving postoperative exams in the two hospitals is the same, and the alternative hypothesis is that the proportion is lower in Cutter Memorial Hospital. The pooled proportion is (90+110)/(200+200) = 0.5. The standard error of the difference between proportions is sqrt((0.5*0.5/200) + (0.5*0.5/200)) = 0.0707. The test statistic is (0.9 - 1.1) / 0.0707 = -2.83, which corresponds to a p-value of 0.0023 using a standard normal distribution. Since this is a left-tailed test (looking for evidence that the proportion is lower in Cutter Memorial Hospital), we can reject the null hypothesis at the 0.05 level of significance, and conclude that there is significant evidence that the proportion of patients receiving postoperative exams is lower in Cutter Memorial Hospital than in Paymor Hospital. The closest option is B) 0.0228.

In a Random Sample of Patient Records in Cutter Memorial