Discussion:
Comparison of mean tread wear of two brands of car by paired students t test.
Q: 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 8 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 On inches) is recorded, as shown in Table .
| Car |
Brand 1 |
Brand 2 |
Difference
(Brand 1 - Brand 2) |
| 1 |
0.201 |
0.193 |
0.008 |
| 2 |
0.368 |
0.315 |
0.053 |
| 3 |
0.334 |
0.235 |
0.099 |
| 4 |
0.332 |
0.332 |
0 |
| 5 |
0.367 |
0.233 |
0.134 |
| 6 |
0.291 |
0.349 |
-0.058 |
| 7 |
0.357 |
0.342 |
0.015 |
| 8 |
0.366 |
0.41 |
-0.044 |
Based on these data. can the consumer group conclude. at the 0.10 leiel of sioniticanct that the mean tread wears of the brands differAnswer this question by performing a hmothesis test regarding lid. the population mean difference in tread Wear for the two brands of tires. Assume thatthis 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 dedmal places and round your answers as spedfied in the table.
The null hypothesis:
The alternative hypothesis:
The value of the test statistic:
The two critical values at the 0.10 level of significance:
At the 0.10 level can the consumer group conclude than the mean tread wears of the brand differ