Question

Use the given degree of confidence and Sample data to construct a confidence interval for the population proportion P. Of 140 adults selected randomly from one Town, 35 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

A)15.6%

B)16.5%

C)19.0%

D)17.8%

Answer 1

CI = (0.156, 0.344)

Explanation:

Confidence interval = proportion ± margin of error

CI = p ± ME

The proportion is:

p = x / n

p = 35/140

p = 0.25

Margin of error = critical value × standard error

ME = CV × SE

n > 30, so we can approximate CV with a normal distribution. At P = 99%, CV = 2.576.

SE = √(pq / n)

SE = √(0.25 (1 − 0.25) / 140)

SE = 0.037

So the margin of error is:

ME = 2.576 × 0.037

ME = 0.094

So the confidence interval is:

CI = 0.25 ± 0.094

CI = (0.156, 0.344)