Question

The Economic Policy Institute periodically issues reports on worker’s wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39?
b. What is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean, $27.83?
c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? Why?

Answer 1

Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for each.
As for why, look at SEm for each.