Question

Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence

A) 0.426

B)0.442

C)0.425

D)0.421

Answer 1

(0.426, 0.574)

Explanation:

Confidence interval = proportion ± margin of error

CI = p ± ME

The proportion is:

p = x / n

p = 55/110

p = 0.5

Margin of error = critical value × standard error

ME = CV × SE

n > 30, so we can approximate CV with a normal distribution. At P = 88%, CV = 1.55.

SE = √(pq / n)

SE = √(0.5 (1 − 0.5) / 110)

SE = 0.048

So the margin of error is:

ME = 1.55 × 0.048

ME = 0.074

So the confidence interval is:

CI = 0.5 ± 0.074

CI = (0.426, 0.574)