hypothesis testing

A researcher uses data from a sample of 3294 full-time workers in the US to investigate whether women
are systematically underpaid compared to men.
(a) Estimate the mean hourly wage in the population of men and of women.
(b) Estimate the variance in the hourly wage in the population of men and of women.
(c) Test the hypothesis that average female hourly wage is less than that of men assuming the variances are equal
(d) Examine whether the assumption of equal variances is correct and make any appropriate adjustments to your test.
(e) Does this answer the researcherís original question? If not how could one (at least partially) correct for this?