EXAMPLE 6 The Phe-Mycin Case: Drug Side Effects Consider estimating the proportion of all patients who would experience nausea as a side effect of taking the new antibiotic Phe-Mycin. Suppose the drug company wishes to find the size of the random sample that is needed in order to obtain a 2 percent margin of error with 95 percent confidence. In Example 4 we employed a sample of 200 patients to compute a 95 percent confidence interval for p. This interval, which is [.122, .228], makes us very confident that p is between 122 and .228. Because 228 is the reasonable value of p that is closest to .5, the largest reasonable value of p(1 - p) Is .228(1 - 228) = .1760, and thus the drug company should take a sample of " = p(1 - p) = 1760 -= 1.691 (rounded up) patients. Suppose that experience indicates that a population proportion p is at least .75. Then, .75 is the reasonable value of p that is closest to .5, and we would use the largest reasonable value of p(1 - p), which is .75(1 - .75)= .1875. ACTIVITY In each of the following cases, compute 95 percent, 98 percent, and 99 percent confidence intervals for the population proportion p. a. p = .4 and n = 100 b. p =.1 and n = 300 C. p =.9 and n = 100 d. p = .6 and n = 50 END OF MODULE E O