Hypothesis Testing and Paired Comparisons
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Hypothesis test for the difference of population means: Paired comparisons
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Though the two brands have been comparable in the past, some technological advances were recently made in the Brand 2 manufacturing process, and the consumer group is testing to see if Brand 2 will outperform Brand 1. 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 in Table 1.
Car Brand 1 Brand 2 Difference
(Brand 1 - Brand 2)
1 0.318 0.253 0.065
2 0.278 0.156 0.122
3 0.297 0.248 0.049
4 0.362 0.271 0.091
5 0.324 0.313 0.011
6 0.286 0.331 -0.045
7 0.338 0.258 0.08
8 0.396 0.248 0.148
9 0.363 0.339 0.024
10 0.36 0.211 0.149
11 0.223 0.273 -0.05
12 0.291 0.227 0.064
Based on these data, can the consumer group conclude, at the level of significance, that the mean tread wear of Brand 1 exceeds that of Brand 2? 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 one-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.)
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Solution Summary
The solution uses hypothesis tests and paired comparisons to test for the difference of population means.
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