Question

A national caterer determined that​ 87% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the​ caterer's food. If ModifyingAbove p with caret is the sample proportion saying that the food is​ delicious, what is the mean of the sampling distribution of ModifyingAbove p with caret​? A. 0.19 B. 0.42 C. 1.25 D. 0.87

Answer 1

(D)0.87

Explanation:

DEFINITION

The mean of the sampling distribution of the sample proportion is equal to the population proportion.

Given that out of the random sample of 144, 87% said that it was delicious

Therefore, the Population proportion = 87%

The sample size of 144 from 5000 will have proportion
`\hat{p}` which will follow a normal distribution with mean p = 87%

Hence the mean of the sampling distribution of
`\hat{p}` is 0.87