Question

The horizontal axis in the sampling distribution of ^p represents all possible sample proportions from a simple random sample of size n.

(a)what percent of sample proportions results in 75% of confidence interval that includes the population proportion?

(b)what percent of sample proportions results in 75% of confidence interval that does not include the population proportion?

Answer 1

a) Suppose we draw many random samples of size n from the same population and suppose we obtain 75% of confidence interval for the population proportion to each samples then we have n confidence interval for the population proportion.

Out of n confidence intervals 75% of them include the true population proportion.

that means we have 75 percent of sample proportions results in 75% of confidence interval that includes the population proportion.

b) This also implies that ( 100 - 75) = 25 percent of sample proportions results in 75% of confidence interval that does not include the population proportion