The Bureau of Labor Statistics shows that the average insurance cost to a company per employee per hour is $1.84 for managers and $1.99 for professional specialty workers. Suppose these figures were obtained from 14 managers and 15 professional specialty workers and that their respective population standard deviations are $0.38 and $0.51.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 managers and professional specialty workers. Use a 2% level of significance.