Question

According to the Bureau of Labor Statistics, 71.9% of Young women enroll in college directly after high school graduation. Suppose a random sample of 200 female high school graduates is selected and the proportion who enroll in college is obtained.

a. What value should we expect for the sample proportion?

b. What is the standard error?

c. What effect would increasing the sample size to 500 have on the standard error?

Answer 1

a. The expected value for the sample proportion can be calculated as the population proportion: 71.9%, so we expect that approximately 71.9% of the 200 female high school graduates will enroll in college directly after high school graduation.

Expected value = population proportion * sample size = 0.719 * 200 = 143.8

Therefore, we expect approximately 144 female high school graduates to enroll in college directly after high school graduation.

b. The standard error of the sample proportion can be calculated as:

SE = sqrt[p(1-p)/n], where p is the population proportion and n is the sample size.

SE = sqrt[0.719(1-0.719)/200] = 0.033

Therefore, the standard error is 0.033.

c. The standard error is inversely proportional to the square root of the sample size. Increasing the sample size from 200 to 500 would reduce the standard error:

SE = sqrt[0.719(1-0.719)/500] = 0.023

Therefore, the standard error would decrease to 0.023 if the sample size increased to 500.