Question

Consider a hypothetical experiment in which investigators randomly selected 58 men from the membership list of the Sacramento Valley Motorist Society and then randomly assigned each man either to a sports utility vehicle (each one the same model and year and with the same amount of cumulative miles) or to a sedan (each one also exactly like the other). The men, 29 in each group, were instructed to drive these cars 100 miles on Interstate 5 in California, ostensibly to test for comfort of the driving experience. However the investigators’ real interest was in whether average speeds along the 100 miles might be different between the SUVs and the sedans. Unbeknownst to the drivers, all the motor vehicles were equipped with devices monitoring speed, acceleration, and other variables. The experiment yielded the following data:

	SUV Speed	Sedan Speed
mean	69.95mph	61.58mph
sd	6.19mph	7.25mph
n	29	29

(i)

Calculate a 99 percent confidence interval for the difference between the mean speeds of the SUVs and the sedans.

(ii)

How do we interpret the results?

Among the answer choices that follow, CHOOSE THE BEST COMBINATIONS OF THE OPTIONS GIVEN IN (i) AND (ii) AND (iii).

Group of answer choices

a.

(i)

(3.19, 13.15)

(ii)

We are 99 percent confident that among the men of the Motorist Society, the average difference in speeds between those driving SUVs and those driving sedans is 3.19 to 13.15 miles per hour.

b.

(i)

(3.19, 13.15)

(ii)

We are 99 percent confident that among drivers of SUVs and sedans, the average difference in speed between the SUVs and the sedans is 3.19 to 13.15 miles per hour.

c.

(i)

(3.53, 12.81)

(ii)

We are 99 percent confident that among drivers of SUVs and sedans, the average difference in speed between the SUVs and the sedans is 3.53 to 12.81 miles per hour.

d.

(i)

(3.53, 12.81)

(ii)

We are 99 percent confident that among the men of the Motorist Society, the average difference in speeds between those driving SUVs and those driving sedans is 3.53 to 12.81 miles per hour.

e. None of the above answers sets is correct.

Answer 1

Page No Data mean sd SUV Speed Gg. 95 mph 6.19 mph Sedan Speed 6158mph 7.25mph. D29 23 | 99% CI for the difference beth mean speed of the suy and the sedan I (5,-*2) I taiz,nt. | s² s2 ni nz (69.95-61158) 1 to 0228 (8.19)? (7.2512 29 29 $ 8. 3 7 2.76 X 1.7702 8.37 4.8857 (8.37-4.8857, 8.37+ 4.8857) (8.4843, 4.8857) 3.4843 el the 4.8857 (3.4843 13.2557) 3.48813 < elite <-13.2557 le. None of the above ans. sets is correct. We are 99% confident that among the men of the motorist society, the average difference in speeds beth, those driving sur's and those driving sedans is 3.4843 to 13.2557 mph.