Question

Suppose we collect a simple random sample of 200 registered voters from a large city. We find that 25% of the voters in the sample are Independents. Find a 95% confidence interval for the percentage of registered voters in the city that are Independents. Round your answer to at least two decimal places.

Answer 1

0.05<x<0.06

Explanation:

The formula for calculating the confidence interval is expressed as;

CI = p' ±z * √p(1-p)/n

z is the z score at 95% CI

p is the proportion of the independent sample

n is the sample size

p' = X/n

p' = 0.25/200

p' = 0.00125

Given

z = 1.96

p = 25% = 0.25

n= 200

Substitute into the formula;

CI = p' ±1.96 *√0.25(1-0.25)/200

CI = p' ±1.96 * √0.25(0.75)/200

CI = p' ±1.96 * 0.0306

CI = p' ±0.0605

CI = 0.00125 ±0.0605

CI = (0.048, 0.06175)

CI = (0.05, 0.06)

0.05<x<0.06