Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

Question

Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

Answer 1

phat = sample proportion = 30/150 = 0.2

n = sample size = 150

z-critical value for 99% CI = 2.58

CI = phat +/- z-critical value * sqrt(phat*(1-phat)/n)

= 0.2 +/- 2.58 * sqrt(0.2*0.8/150)