In a production facility, an accurate estimate of man hours needed to complete a task is crucial to management in making such decisions as the proper number of workers to hire, an accurate deadline to quote a client, or cost-analysis decisions regarding budgets. A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect the drums in future projects. To accomplish this, data for 35 boilers were collected. In addition to man-hours (y), the variables measured were boiler capacity (x₁ = Ib/hr), boiler design pressure (x₂ = pounds per square inch or psi), boiler type (x₃ = 1 if industry field erected, 0 if utility field erected), and drum type (x₄ = 1 if steam, 0 if mud). The data are provided in the table on page 598. A MINITAB printout for the model   is shown on page 597

a. Conduct a test for the global utility of the model. Use a = .01

b. Both a 95% confidence interval for E(y) and a 95% prediction interval for y when x₁ = 150,000, x₂ = 500, x₃ = 1 and x₄ = 0 are shown at the bottom of the MINITAB printout. Interpret both of these intervals.