Question

Consider a population proportion p = 0.17. [You may find it useful to reference the z table.]

a. Calculate the standard error for the sampling distribution of the sample proportion when n = 25 and n = 55? (Round your final answer to 4 decimal places.)

b. Is the sampling distribution of the sample proportion approximately normal with n = 25 and n = 55?

Answer 1

Part a

We are given

p = 0.17

q = 1 - p = 1 - 0.17 = 0.83

For n = 25

Standard error = sqrt(pq/n) = sqrt(0.17*0.83/25) = 0.0751

For n = 55

Standard error = sqrt(pq/n) = sqrt(0.17*0.83/55) = 0.0507

Part b

The sampling distribution of the sample proportion approximately normal with n = 25 and n = 55, because we know that the sampling distribution follows an approximately normal distribution although population is not normal, or it is skewed in nature, or sample size is small or large.