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 of8

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 for20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1.

CarBrand 1Brand 2Difference

(Brand 1 - Brand 2)

1 0.239 0.212 0.027

2 0.221 0.214 0.007

3 0.305 0.126 0.179

4 0.303 0.180 0.123

5 0.380 0.244 0.136

6 0.326 0.181 0.145

7 0.222 0.120 0.102

8 0.355 0.286 0.069

Based on these data, can the consumer group conclude, at the0.05 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regardingd

(which is 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.

The null hypothesis: H0:

The alternative hypothesis: H1:

The type of test statistic:(Choose one)

Z

t

Chi square

F

The value of the test statistic:

(Round to at least three decimal places.)

The two critical values at the0.05

level of significance:

(Round to at least three decimal places.)and

At the 0.05 level, can the consumer group conclude that the mean tread wears of the brands differ?

Yes

No