1. According to the bureau of labor statistics, the mean hourly wage in april 1996 was $14.49 for transportation and public utility workers and $12.79 for manufacturing workers. Assume that these two estimates are based on random samples of 1000 and 1200 workers taken, respectively from the two populations. further assume that the standard deviations of the two populations are $1.85 and $1.40, respectively. test at the 2.5% significance level if the mean hourly wages for transportation and public utility workersin april 1996 was higher than that of manufacturing workers.

(show all 5 steps for the hypothesis testing)

2. The lottery commissioner's office in a state wanted to find if the percentages of men and women who play the lottery are often different. A sample of 500 men taken by the commisioner's office showed that 165 of them play the lottery often. Another sample of 300 women showed that 69 of them play the lottery often. testing at the 1% significance level, can you conclude that the proportions of all men and all women who play the lottery often are different?

(show all 5 steps for hypothesis testing)