An auto repair store sells a certain brand of all-season tires. They are interested in whether, for front- wheel drive cars, the wear on the front tires is different from than that on the rear tires over the course of a year. They install sets of 4 identical new tires on 30 front-wheel drive cars. After one year, they measure the tread depth (in units of 32") on one randomly selected front tire and on one randomly selected rear tire from each car. Their data are available in the file tire.csv. You may assume that tread depths are normally distributed with common standard deviation. a) Do you expect tread depths to be independent? Explain. b) Construct a 95% confidence interval for the mean difference between tread depth of front tires and tread depth of rear tires over the course of the year. c) Based on your confidence interval in b), does the wear differ for front and rear tires? Explain.
An auto repair store sells a certain brand of all-season tires. They are interested in whether, for front- wheel drive cars, the wear on the front tires is different from than that on the rear tires over the course of a year. They install sets of 4 identical new tires on 30 front-wheel drive cars. After one year, they measure the tread depth (in units of 32") on one randomly selected front tire and on one randomly selected rear tire from each car. Their data are available in the file tire.csv. You may assume that tread depths are normally distributed with common standard deviation. a) Do you expect tread depths to be independent? Explain. b) Construct a 95% confidence interval for the mean difference between tread depth of front tires and tread depth of rear tires over the course of the year. c) Based on your confidence interval in b), does the wear differ for front and rear tires? Explain.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Transcribed Image Text:An auto repair store sells a certain brand of all-season tires. They are interested in whether, for front-
wheel drive cars, the wear on the front tires is different from than that on the rear tires over the course
of a year. They install sets of 4 identical new tires on 30 front-wheel drive cars. After one year, they
measure the tread depth (in units of 32") on one randomly selected front tire and on one randomly
selected rear tire from each car. Their data are available in the file tire.csv. You may assume that tread
depths are normally distributed with common standard deviation.
a) Do you expect tread depths to be independent? Explain.
b) Construct a 95% confidence interval for the mean difference between tread depth of front tires
and tread depth of rear tires over the course of the year.
c) Based on your confidence interval in b), does the wear differ for front and rear tires? Explain.
Transcribed Image Text:"car.id" "front.depth" "rear.depth"
1 8.44 8.46
2 8.39 8.5
3 8.38 8.45
4 8.4 8.36
5 8.51 8.44
6 8.44 8.46
7 8.47 8.58
8 8.53 8.55
9 8.46 8.55
10 8.38 8.44
11 8.35 8.45
12 8.34 8.55
13 8.4 8.51
14 8.46 8.46
15 8.45 8.51
16 8.4 8.47
17 8.36 8.45
18 8.45 8.49
19 8.48 8.55
20 8.43 8.44
21 8.36 8.41
22 8.46 8.48
23 8.4 8.52
24 8.41 8.57
25 8.42 8.58
26 8.38 8.48
27 8.4 8.45
28 8.44 8.43
29 8.45 8.49
30 8.37 8.49
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