A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Difference Car Brand 1 Brand 2 (Brand 1 - Brand 2) 1 0.376 0.373 0.003 2 0.321 0.288 0.033 0.249 0.256 -0.007 4 0.344 0.341 0.003 0.230 0.221 0.009 0.268 0.256 0.012 7 0.347 0.363 -0.016 0.312 0.296 0.016 9 0.293 0.289 0.004 10 0.385 0.390 -0.005 11 0.274 0.240 0.034 12 0.323 0.321 0.002 Table 1 Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding u, (which is µ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires.
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Difference Car Brand 1 Brand 2 (Brand 1 - Brand 2) 1 0.376 0.373 0.003 2 0.321 0.288 0.033 0.249 0.256 -0.007 4 0.344 0.341 0.003 0.230 0.221 0.009 0.268 0.256 0.012 7 0.347 0.363 -0.016 0.312 0.296 0.016 9 0.293 0.289 0.004 10 0.385 0.390 -0.005 11 0.274 0.240 0.034 12 0.323 0.321 0.002 Table 1 Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding u, (which is µ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type
of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of
each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of
the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1.
Difference
Brand 2 (Brand 1 - Brand 2)
Car Brand 1
0.376
0.373
0.003
2
0.321
0.288
0.033
3
0.249
0.256
-0.007
4
0.344
0.341
0.003
5
0.230
0.221
0.009
6
0.268
0.256
0.012
7
0.347
0.363
-0.016
8
0.312
0.296
0.016
9.
0.293
0.289
0.004
10
0.385
0.390
-0.005
11
0.274
0.240
0.034
12
0.323
0.321
0.002
Table 1
Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the mean tread wears of the brands differ? Answer this question
by performing a hypothesis test regarding u (which is u with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires.
Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed.
Transcribed Image Text:by performing a hypothesis test regarding u, (which is u with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires.
Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed.
Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as
specified in the table. (If necessary, consult a list of formulas.)
The null hypothesis:
H, : 0
H, :0
Н
1
The alternative hypothesis:
The type of test statistic:
|(Choose one) ♥
O<O
The value of the test statistic:
(Round to at least three
decimal places.)
The two critical values at the
0.05 level of significance:
Dand
||and |
(Round to at least three
decimal places.)
At the 0.05 level, can the consumer group
conclude that the mean tread wears of the brands
Yes
No
differ?
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