A oonsumer products testing group is evaiuating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerabty depending on the type
of car, and the group is trying to eliminate his 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 ofthe cars chosen at random to have Brand 1 on the left front wheei, and the rest to have Brand 2 there. After aEE of
the cars are driven over the standard test oourse for 20,000 miles, the amount of tread wear (in inches] is recorded, as shown in Table 1. Car Brand 1 Brand 2 {Brangi‘qe-ﬂlainrgﬁd 2) .
1 0.370 0.429 -0.059
2 0.362 0.309 0.053 @
3 0.343 0.266 0.077
4 0.291 0.345 -0.054
5 0.355 0.341 0.015
5 0.241 0.192 0.049
2 0.399 0.355 0.043
0 0.320 0.240 0.030 Table 1 Based on these data, can the consumer group oonclude, at the 0.10 level of signiﬁcanoe, that the mean tread wears of the brands differ? Answer this question
by performing a hypothesis test regarding pd (which is p. 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 Feast three decimal piaces and round your answers as
specified in the table. (If necessary, oonsult a list of formulas.) ‘H lid 0 p The null hypothesis: Hn .