A 95% confidence interval for the population proportion of professional tennis players who earn more than 2 million dollars a year is found to be between .82 and .88. Given this information, the sample size that was used was approximately:
A) 545
B) 382
C) 233
D) 387
E) 480

Question

Quizplus · Accepted Answer

The formula for a confidence interval for a proportion is p̂ ± Z*(√(p̂(1-p̂)/n)). Given the interval (.82, .88), the sample proportion p̂ is (0.82+0.88)/2 = 0.85. The margin of error is 0.88 - 0.85 = 0.03. Using a Z-score of 1.96 for 95% confidence, solve 1.96*(√(0.85*0.15/n)) = 0.03 to find n ≈ 545.

A 95% Confidence Interval for the Population Proportion of Professional