AP STATISTICS
UNIT 9
1. Cars and trucks lose value the more they are driven. Can we predict the price of a used Ford F150 SuperCrew 4×4 if we know how many miles it has on the odometer? Research group 1
collect a random sample of 16 used Ford F-150 SuperCrew 4×4s was selected from among those
listed for sale on a particular Web site. The number of miles driven and price were recorded for
each of the trucks. The data is shown below, where the price of such a vehicle is the response
variable.
MILES DRIVEN
PRICE (DOLLARS)
70,583
21,994
129,484
9,500
29,932
29,875
29,953
41,995
24,495
41,995
75,678
28,986
8,359
31,891
4,447
37,991
34,077
34,995
58,023
29,988
44,447
22,896
68,474
33,961
144,162
16,883
140,776
20,897
29,397
27,495
131,385
13,997
A least-squares regression analysis of the data is shown below.
(a) Research group 1 wishes to construct a 98-percent confidence interval for the slope of the
population regression line.
i. In the context of the problem, identify the population to which a confidence interval
for the slope of the true regression line can be generalized.
ii. Assume that the conditions for inference have been met. Construct research group
1’s confidence interval.
iii. Interpret your results from part (a)(ii).
iv. Determine the margin of error of your results from part (a)(ii).
(b) To attract individuals that would otherwise not purchase used vehicles, the Web site claims
that there is no relationship between the miles driven and the price of their Ford F-150s.
Another research group, research group 2, wishes to test this claim using a test for the slope
of the population regression line at 𝛼 = 0.01.
i. Identify the null and alternative hypotheses of the test.
ii. Assume that the conditions for inference have been met. Does the data provide
convincing evidence that there is, in fact, a relationship between the miles driven and
the price of the Web site’s Ford F-150s?
iii. Justify your answer from part (b)(i).
iv. Describe a Type II error in the context of the problem.