# Question

Refer to Exercise 10.56, in which a random sample of six cars was selected to test a gasoline additive. The six cars were driven for 1 week without the gasoline additive and then for 1 week with the additive. The data reproduced here from that exercise show miles per gallon without and with the additive.

Suppose that instead of the study with 6 cars, a random sample of 12 cars is selected and these cars are divided randomly into two groups of 6 cars each. The cars in the first group are driven for 1 week without the additive, and the cars in the second group are driven for 1 week with the additive. Suppose that the top row of the table lists the gas mileages for the 6 cars without the additive, and the bottom row gives the gas mileages for the cars with the additive. Assume that the distributions of the gas mileages with or without the additive are (approximately) normal with equal but unknown standard deviations.

a. Would a paired sample test as described in Section 10.4 be appropriate in this case? Why or why not? Explain.

b. If the paired sample test is inappropriate here, carry out a suitable test of whether the mean gas mileage is lower without the additive. Use α = .025.

c. Compare your conclusion in part b with the result of the hypothesis test in Exercise 10.56.

Suppose that instead of the study with 6 cars, a random sample of 12 cars is selected and these cars are divided randomly into two groups of 6 cars each. The cars in the first group are driven for 1 week without the additive, and the cars in the second group are driven for 1 week with the additive. Suppose that the top row of the table lists the gas mileages for the 6 cars without the additive, and the bottom row gives the gas mileages for the cars with the additive. Assume that the distributions of the gas mileages with or without the additive are (approximately) normal with equal but unknown standard deviations.

a. Would a paired sample test as described in Section 10.4 be appropriate in this case? Why or why not? Explain.

b. If the paired sample test is inappropriate here, carry out a suitable test of whether the mean gas mileage is lower without the additive. Use α = .025.

c. Compare your conclusion in part b with the result of the hypothesis test in Exercise 10.56.

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