Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will ofa minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of guncontrol legislation. How many citizens would need to be sampled if a 99% confidence interval was desired toestimate the true proportion to within 1%?
A) 16,318
B) 17,240
C) 16,577
D) 15,251

Question

Quizplus · Accepted Answer

The sample size needed to estimate the true proportion to within 1% with a 99% confidence interval is 16,318. This is calculated using the formula n = (Z^2 * p * q) / e^2, where Z is the z-score for the desired confidence level, p is the sample proportion, q is 1 - p, and e is the margin of error. In this case, Z = 2.576, p = 0.5625, q = 0.4375, and e = 0.01. Plugging these values into the formula gives n = 16,318.

Many People Think That a National Lobbyʹs Successful Fight Against