A random sample of 80 observations results in 50 successes.

Question

A. Construct the 95% confidence Interval for the population of successes.

Confidence interval: _______ to ________

B. Construct the 95% confidence Interval for the population of failures.

Confidence interval: _______ to ________

Answer 1

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

critical z for 95% confidence interval = 1.96

sample size = 80

95% CI = phat +/- 1.96 * square root(phat*(1-phat)/80)

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

same critical z and same 95% CI formula apply