In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from aquarter-system to a semester-system. How many students should be polled so that we can estimate p towithin 0.09 using a 99% confidence interval?
A) 205
B) 182
C) 261
D) 114

Question

Quizplus · Accepted Answer

The sample size needed to estimate the proportion p to within 0.09 using a 99% confidence interval is given by:n = (Z^2 * p * q) / e^2where Z is the z-score for the desired confidence level, p is the estimated proportion, q is the complement of p (1-p), and e is the margin of error.For a 99% confidence level, Z = 2.576. The estimated proportion is not given, so we will use p = 0.5 (which gives the largest sample size). The margin of error is 0.09.Plugging these values into the formula, we get:n = (2.576^2 * 0.5 * 0.5) / 0.09^2n = 204.6Rounding up to the nearest whole number, we get a sample size of 205.

In a College Student Poll, It Is of Interest to Estimate