A pilot sample of 75 items was taken, and the number of items with the attribute of interest was found to be 15. How many more items must be sampled to construct a 99% confidence interval estimate for p with a 0.025 margin of error?
A) 1512
B) 1612
C) 1698
D) 1623

Question

Quizplus · Accepted Answer

To find the required sample size for a 99% confidence interval with a margin of error of 0.025, use the formula for sample size: n = (Z^2 * p * (1-p)) / E^2. Here, Z is the Z-score for 99% confidence (2.576), p is the sample proportion (15/75 = 0.2), and E is the margin of error (0.025). Calculating this gives approximately 1698 total samples needed. Since 75 have already been sampled, 1698 - 75 = 1623 more items are needed.

A Pilot Sample of 75 Items Was Taken, and the Number