To investigate possible sex discrimination in a firm, a sample of \(100 \mathrm{men}\) and 64 women with similar job descriptions is selected at random. A summary of the resulting monthly salaries follows:

a. What do these data suggest about wage differences in the firm? Do they represent statistically significant evidence that average wages of men and women are different? (To answer this question, first, state the null and alternative hypotheses; second, compute the relevant \(t\)-statistic; third, compute the \(p\)-value associated with the \(t\)-statistic; and, finally, use the \(p\)-value to answer the question.)

b. Do these data suggest that the firm is guilty of sex discrimination in its compensation policies? Explain.

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Average Salary (Y) Standard Deviation (sy) n Men Women $3100 $2900 $200 100 $320 64