Question

The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011. Assume that the standard deviation for male graduates is $2.30, and for female graduates, it is $2.05.

(a)	What is the sampling distribution of x for a random sample of 50 male college graduates? If required, round your answer to four decimal places.
(b)	What is the sampling distribution of x for a random sample of 50 female college graduates? If required, round your answer to four decimal places

Answer 1

Solution:

Given:

The institute reported that entry-level wages for male college graduates were $21.68 per hour and

for female college graduates were $18.80 per hour in 2011.

The standard deviation for male graduates is $2.30, and for female graduates, it is $2.05.

That is for male graduates :

and for female graduates :

Part a) Find  the sampling distribution of x for a random sample of 50 male college graduates.

Since sample size n = 50 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) Find  the sampling distribution of x for a random sample of 50 female college graduates.

Since sample size n = 50 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: