Statistics Problem

Question

A survey of 875 voters in one state reveals that 421 favor approval of an issue before the legislature. Construct the 90% confidence interval for the true proportion of all voters in the state who favor approval.

Answer 1

The 90% confidence interval for a single proportion is:

phat +/- sqrt[(phat)(1-phat)/n)] * z-critical

where phat is the sample proportion = 421/875 = 0.485

n = sample size = 875

z-critical = z-value for 90% confidence interval = 1.645 (since 90% confidence interval is middle 90% area of normal curve, thus area between z corresponding to 0.05 and 0.95 probabilities, so z-critical is z value corresponding to 0.95 probability).

so 90% CI =

0.485 +/- sqrt[(0.485)(0.515)/875)] * 1.645 = 0.485 +/- 0.028 = (0.457,0.513)