Question

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 performance measure is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines are listed in the table below. Suppose that standard gas turbines have heat rates with a standard deviation of 1,500 kJ/kWh. Is there sufficient evidence to indicate that the heat rates of the augmented gas turbine engine are more variable than the heat rates of the standard gas turbine engine? Test using a = .05.

Short answer

There is insufficient information to infer that the mean heat rates of a gas turbine with pressure inlet fogging exceeds 1,500 KJ/kWh when the alpha is 0.05.

Step-by-step solution

The variable is the Gas turbine

There is insufficient information to infer that the mean heat rates of a gas turbine with pressure inlet fogging exceeds 1,500 KJ/kWh when the alpha is 0.05.

$$\begin{gathered} \text{We may use the following direct command for t testing:} \\ \text{n = 61} \\ mu=1500\#\#populationmean \\ \#\#totest:Ho:mu=1,500vsH1:mu>1500 \\ t.test(GASTURBINE,mu=1500,alternative="greater",conf.level=0.05,paired=FALSE) \end{gathered}$$

One-Sample t-test

$$\begin{gathered} \text{Data: GAS TURBINE} \\ \text{t = alternative hypothesis: true mean is greater than 1500} \\ \text{5 percent confidence interval:} \\ 11478.69Inf \\ \text{Sample estimates:} \\ \text{Mean of x = 11132.93} \end{gathered}$$

If the p-value is smaller than the alpha value, we reject Ho. We reject Ho.

There is insufficient information to infer that the mean heat rates of a gas turbine with pressure inlet fogging exceeds 1,500 KJ/kWh when the alpha is 0.05.

The type 1 and type 2 error:

We reject Ho when it is true is a type 1 error here; we reject Ho that is type error occurs, and a type 2 error is the mean hears rates of a gas turbine with pressure inlet fogging exceeding 1,500 KJ/kWh when alpha is 0.05.

$\text{The fail to reject Ho.}$