Question

1. Our university periodically issues reports on wages of entry-level workers. We reported that entry-level wages for male college graduates were $23.68 per hour and for female college graduates were $20.80 per hour in 2019. Assume that the standard deviation for male graduates is $2.40 and for female graduates it is $2.15.
   1. What is the sampling distribution of x for a random sample of 50 male college graduates?
   2. What is the sampling distribution of x for a random sample of 50 female college graduates?
   3. In which of the two cases is the standard error smaller?

Answer 1

Solution:

Given:

Male college graduates:

Mean = per hour

Standard Deviation =

Female college graduates:

Mean = per hour

Standard Deviation =

Part a) What is the sampling distribution of x for a random sample of 50 male college graduates?

Sample size = n = 50

Since sample size n = 50 ( > 30) is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Part b) What is the sampling distribution of x for a random sample of 50 female college graduates?

Since sample size n = 50 ( > 30) is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Part c) In which of the two cases is the standard error smaller?

The standard error of entry-level wages for female graduates is less than that of male graduates.

Thus the standard error of  entry-level wages for female graduates is smaller.