Problem 24E

Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 7.40 (p. 378). The researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Summary statistics on heat rate (kilojoules per kilowatt per hour) for each of the three types of gas turbines are shown in the Minitab printout (at the top of the next column).

a. Is there sufficient evidence of a difference between the mean heat rates of traditional augmented gas turbines and aeroderivative augmented gas turbines? Test using α = .05.

b. Is there sufficient evidence of a difference between the mean heat rates of advanced augmented gas turbines and aeroderivative augmented gas turbines? Test using α = .05.

Answer

Step 1 of 2

(a)

Summary statistics on heat rate (kilojoules per kilowatt per hour) for each of the three types of gas turbines are shown in the Minitab printout.

Is there sufficient evidence of a difference between the mean heat rates of traditional augmented gas turbines and aeroderivative augmented gas turbines?

Test using

Let the mean heat rates of traditional augmented gas turbines and the mean heat rates of aeroderivative augmented gas turbines.

To determine if there is a difference between the mean heat rates of traditional augmented gas turbines and the mean heat rates of aeroderivative augmented gas turbines, we do following hypothesis test:

Let us now consider hypothesis tests about the difference between the means of two populations

when the population standard deviations and are unknown.

we will use the sample standard deviations and to estimate and and replace with .

The hypothesis tests about the difference between two population means. Using to denote the hypothesized difference between and , the form for a hypothesis test are as follows:

Rejection rule for two tail test: The Critical Value Approach,

……..(1)

The test statistic for hypothesis tests about unknown

……………(2)

And has degrees of freedom.

The pooled sampled variance

The test statistic for hypothesis tests using equation (2),

…………(3)

The rejection region requires in the two tail of the with

degrees of freedom.

From Table III, Appendix D,

………(4)

From equation (3) and (4) we can see that the observed value of the test statistic does not fall in the rejection region.

Since the rejection rule is not satisfying here,

[not possible condition]

Hence is not rejected and there is insufficient evidence to indicate that there is a difference between the mean heat rates of traditional augmented gas turbines and the mean heat rates of aeroderivative augmented gas turbines at