A random sample of 80 observations results in 50 successes.

Question

A. Construct the 95% confidence interval for the population proportion of successes.

B. Construct the 95% confidence interval for the population proportion of failures.

Answer 1

sample proportion of successes (phat) = 50/80 = 0.625

z-critical for 95% CI is 1.96

CI = 0.625 +/- 1.96 * sqrt(0.625*0.375/80)

sample proportion of failures (phat) = 30/80 = 0.375

CI = 0.375 +- 1.96 * sqrt(0.375*0.625/80)