A National Adult Literacy Survey revealed that males with a postgraduate degree had a sample mean salary of $61,340 (with standard error SM = $2,185), while females with a postgraduate degree had a sample mean salary of $32,227 (with standard error sf = $932). Let µM represent the population mean salary of all males with postgraduate degrees and µF represent the population mean salary of all females with postgraduate degrees.
a. Set up the null and alternative hypotheses for determining whether pM exceeds pF.
b. Calculate the test statistic for the test, part a. [sM-f = √(s2M + s2F).]
c. Find the rejection region for the test using α = .01.
d. Use the results, parts b and c, to make the appropriate conclusion.
For Information: Refer to the Economics of Education Review (Vol. 21, 2002) study of the relationship between education level and earnings, Exercise 7.46.