Solved: Cooling method for gas turbines. Refer to the

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