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# Test Statistics of Consumer Products

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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 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 miles, the amount of tread wear (in inches) is recorded, as shown

Car Brand 1 Brand 2 Difference
(Brand 1 - Brand 2)
1 0.215 0.27 -0.055
2 0.4 0.277 0.123
3 0.347 0.248 0.099
4 0.34 0.206 0.134
5 0.279 0.304 -0.025
6 0.219 0.201 0.018
7 0.399 0.417 -0.018
8 0.254 0.36 -0.106
9 0.262 0.228 0.034
10 0.239 0.188 0.051
11 0.281 0.329 -0.048
12 0.369 0.353 0.016

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

1. The null hypothesis is?
2. The alternative hypothesis is?
3. They type of test statistics is?
4. The value of the test statistics is? (Round to at least three decimal places)
5. The two critical values at the 0.10 level of significance is? (Round to at least three decimal places)
6. At the 0.10 level can the consumer group conclude that the mean tread wears of the brand differ?