People can develop allergic reactions to sulfites, a family of chemical compounds often used for commercial food preservation. Researchers examined a sample of 21 patients with hypertension who had sought treatment regarding some allergic reaction. The published findings state that 9 of them were sensitive to sulfites. How large a sample n would you need to estimate p with margin of error 0.05 with 95% confidence? Use the guess p = 0.50 as the value for p*.

Question

Quizplus · Accepted Answer

Using the formula for sample size, where:
n = (Z^2 * p * (1-p)) / E^2
Z = 1.96 (for 95% confidence)
p* = 0.50
E = 0.05

Substituting the values:
n = (1.96^2 * 0.50 * 0.50) / (0.05^2)
n = 384.16

Rounding up to the nearest whole number, we get n = 385, which is the sample size needed to estimate p with a margin of error of 0.05 at 95% confidence.

People Can Develop Allergic Reactions to Sulfites, a Family of Chemical