The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research were obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of $61,340 (with standard error sx̅ = $2,185), while females with a postgraduate degree have a mean of $32,227 (with standard error sx̅ = $932).

a. The article reports that a 95% confidence interval for μM, the population mean salary of all males with postgraduate degrees, is ($57,050, $65,631). Based on this interval, is there evidence to say that μM differs from $60,000? Explain.

b. Use the summary information to test the hypothesis that the true mean salary of males with postgraduate degrees differs from $60,000. Use a = .05.

c. Explain why the inferences in parts a and b agree.

d. The article reports that a 95% confidence interval for mF, the population mean salary of all females with postgraduate degrees, is ($30,396, $34,058). Based on this interval, is there evidence to say that mF differs from $33,000? Explain.

e. Use the summary information to test the hypothesis that the true mean salary of females with postgraduate degrees differs from $33,000. Use a = .05.

f. Explain why the inferences in parts d and e agree.