A confidence interval was used to estimate the proportion of math majors that are female. A random sample of72 math majors generated the following confidence interval: (0.438, 0.642). Using the information above, whatsize sample would be necessary if we wanted to estimate the true proportion to within 3% using 98%reliability?
A) 1499
B) 1509
C) 1569
D) 1448

Question

Quizplus · Accepted Answer

The sample size needed to estimate the true proportion to within 3% using 98% reliability is 1499. This can be 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 estimated proportion, q is 1 - p, and e is the margin of error. In this case, Z = 2.326 (for a 98% confidence level), p = 0.54 (the midpoint of the confidence interval), q = 0.46, and e = 0.03. Plugging these values into the formula, we get n = (2.326^2 * 0.54 * 0.46) / 0.03^2 = 1499.

A Confidence Interval Was Used to Estimate the Proportion of Math