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 comparing these two proportions, normality of the difference may be assumed because:
A)the populations are large enough to be assumed normal.
B)the probability of success can reasonably be assumed constant.
C)the samples are random, so the proportions are unbiased estimates.
D)nπ ≥ 10 and n(1 - π) ≥ 10 for each sample taken separately.

Question

Quizplus · Accepted Answer

To assume normality in comparing proportions, we need to check whether the sample sizes are large enough which is ensured if nπ ≥ 10 and n(1 - π) ≥ 10. In this case, we have 90 successes out of 200 trials for Cutter Memorial Hospital and 110 successes out of 200 trials for Paymor Hospital. Thus, nπ for both hospitals is 200 x 0.45 = 90 and n(1 - π) is 200 x 0.55 = 110 for both hospitals. So, normality can be assumed. Option A is not correct because the question does not provide any information about the size of the populations. Option B is not correct because the assumption of constant probability of success is not a condition for normality. Option C is not correct because unbiasedness does not guarantee normality.

In a Random Sample of Patient Records in Cutter Memorial