The Bureau of Labor Statistics shows that the average insurance cost to a company per hour worked for an employee by major industry group is $3.22 for construction workers and $3.97 for manufacturing workers. Suppose these figures were obtained from 14 construction workers and 15 manufacturing workers and that their respective population standard deviations are $1.38 and $1.51. Assume that such insurance costs are normally distributed in the population.

a. Calculate a 98% confidence interval to estimate the difference in the mean hourly company expenditures for insurance for these two groups. What is the value of the point estimate?

b. Test to determine whether there is a significant difference in the hourly rates employers pay for insurance between construction workers and manufacturing workers. Use a 2% level of significance.