Question

How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the​ 95% confidence interval of the population proportion

Answer 1

(0.0706, 0.1294)

Explanation:

Confidence interval of a proportion is:

CI = p ± CV × SE

where p is the proportion,

CV is the critical value (z score or t score),

and SE is the standard error.

The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.

Standard error for a proportion is:

SE = √(pq/n)

SE = √(0.1 × 0.9 / 400)

SE = 0.015

The confidence interval is:

CI = 0.1 ± (1.96)(0.015)

CI = (0.0706, 0.1294)

Round as needed.