Hi I need help with the type error

Question

1.62) Cooling method for gas turbines. During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high pressure inlet fogging The performance of a sample of 67 gas turbines augmented with high pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (January 2005). One measure of performance is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines, saved in the GASTURBINE file, are listed in the table. Suppose that a standard gas turbine has, on average, a heat rate of 10,000 kJ/kWh. (a) Conduct a test to determine if the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10,000 kJ/kWh. Use α = .05. (b) Identify a Type I error for this study, then a Type II error.

Answer 1

Hello Felix,

In hypothesis testing a type I error occurs when the null hypothesis is rejected (or alternative is accepted) even though the null hypothesis is true. Using the language of this problem a type I error may be described as follows: Claiming that the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10,000 kj/kwh even though it does not.

Furthermore, a type II error occurs when we do not reject the null hypothesis (or not accept the alternative) even though the alternative hypothesis is true. In this situation a type II error would be to claim that the mean heat rate of gas turbines augmented with high pressure inlet fogging does not exceed 10,000 kj/kwh when in actuality it does.

Hope this helps.