Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 12.19 (p. 726). Recall that you fit a first-order model for heat rate (y) as a function of speed (x₁) , inlet temperature (x₂) , exhaust temperature (x₃) , cycle pressure ratio (x₄) , and airflow rate (x₅) . A Minitab printout with both a 95% confidence interval for E(y) and prediction interval for y for selected values of the x’s is shown below.

a. Interpret the 95% prediction interval for y in the words of the problem.

b. Interpret the 95% confidence interval forE(y)in the words of the problem.

c. Will the confidence interval for E(y) always be narrower than the prediction interval for y? Explain.

95% confidence interval for y here is (12157.9, 13107.1) where the variable setting set at speed = 7500, inlet temperature = 1000, exhaust temperature = 525, cycle pressure ratio = 13.5, and airflow = 10. Given the variable setting, it can be concluded with 95% accuracy that the value of y will lie within the interval (12157.9, 13107.1).

95% confidence interval for E(y) here is (13599.6, 13665.5) where the variable setting set at speed = 7500, inlet temperature = 1000, exhaust temperature = 525, cycle pressure ratio = 13.5, and airflow = 10. Given the variable setting, it can be concluded with 95% accuracy that the value of E(y) will lie within the interval (13599.6, 13665.5).

A prediction interval for y predicts the range in which the individual value of y will lie. While the confidence interval shows the range of values for E(y). Since the prediction interval must also include the uncertainty in estimating the mean plus the variation in estimating an individual value, the prediction interval is always wider than the confidence interval.