Question

A car company advertises that their Super Spiffy Sedan averages 29 mpg (miles per gallon). You randomly select a sample of Super Spiffies from local dealerships and test their gas mileage under similar conditions.

You get the following MPG scores:

33 27 32 34 34 28 27 31

Note: SSx = 63.50

Using alpha =.01, conduct the 8 steps to hypothesis testing to determine whether the actual gas mileage for these cars differs significantly from 29mpg.

Answer 1

The sample size is n = 8. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	33	1089
	27	729
	32	1024
	34	1156
	34	1156
	28	784
	27	729
	31	961
Sum =	246	7628

The sample mean is computed as follows:

  

Also, the sample variance is

Therefore, the sample standard deviation s is

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 29

Ha: μ ≠ 29

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is t_c = 3.499

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |t| = 1.643 < t_c = 3.499, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 29, at the 0.01 significance level.