Suppose we take random samples of 41 carpenters and 41 welders. The sample distribution of annual salaries of full-time carpenters has a mean equal to $24,000 and a standard deviation equal to $2,500. The sample distribution of annual salaries of full-time welders has a mean equal to $25,000 and a standard deviation equal to $3,000.

(4)(a) Test the hypothesis that the mean salary of the welders equals the mean salary of the carpenters, at a 5% level of significance. Use a one tail test.

(5)(b) Test the hypothesis that the mean salaries for the welders and carpenters are within $500 of one another, at a 5% level of significance.