Question

Construct the 99% confidence interval estimate of the population proportion p if the sample size is n=700 and the number of successes in the sample is x=251.

____<p<____

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 251 / 700 = 0.359

1 - = 1 - 0.359 = 0.641

Z_/2 = 2.576

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

= 2.576 * (((0.359 * 0.641) / 700)

Margin of error = E = 0.047

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.359 - 0.047 < p < 0.359 + 0.047

0.312 < p < 0.406