Question

A simple random sample of size n = 1,160 is obtained from a population whose size is n = 1,700,000 and whose population proportion with a specified characteristic is p = 0.24. Describe the sampling distribution of (p) hat.

Answer 1

The sampling distribution of (p) hat in this case can be approximated to a normal distribution with a mean of p=0.24 and a standard deviation of 0.0122.

Step-by-step explanation:

The sampling distribution of (p) hat in this case can be approximated to a normal distribution with a mean of p=0.24 and a standard deviation calculated using the formula sqrt(pq/n).

Given that the sample size n is 1,160 and the population proportion p is 0.24, the standard deviation would be calculated as:

sqrt(0.24*(1-0.24)/1160) = 0.0122.

Hence, the sampling distribution of (p) hat is approximately normal with a mean of 0.24 and a standard deviation of 0.0122.