Question

In a survey conducted with 600 participants across the United States, 450 were found to have studied science in college. If we were to predict the population proportion with a 99.7% confidence, what would the confidence interval be? A. 69.7% to 80.3% B. 73.23% to 76.76% C. 71.46% to 78.53% D. 73.5% to 76.5%

Answer 1

Confidence interval of a population proportion is given by p^ + or - sqrt(p^(1 - p^)/n); where p^ = 450/600 = 0.75 and n = 600
99.7% convidence interval = 0.75 + or - 2.96 x sqrt(0.75(1 - 0.75)/600) = 0.75 + or - 2.96 x sqrt(0.75(0.25)/600) = 0.75 + or - 2.96 x 0.0177 = 0.75 + or - 0.0524 = 0.697 to 0.803 = 69.7% to 80.3%