Question

Assume that a sample is used to estimate a population proportion p. Find the 99% confidence interval for a sample of size 249 with 30 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 30 / 249 = 0.120

Z_/2 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.120 * 0.880) / 249)

= 0.053

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.120 - 0.053 < p < 0.120 + 0.053

0.067 < p < 0.173

(0.067 , 0.173)