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# Hypothesis testing and confidence interval problem

A. *HT* A test was conducted to compare the wearing quality of the tires produced by two tire companies. A random sample of 16 cars is equipped with one tire of Brand X and one tire of Brand Y (the other two tires on each car are not part of the test), and driven for 30 days. The following table gives the amount of wear in thousandths of an inch that resulted (the smaller the number the better the wear quality of the tire). Assume tire wear is normally distributed. At the 1% level of significance, do Brand X tires have better wear quality than Brand Y tires?
B. *CI* Calculate the 98% confidence interval estimate for the mean difference. Does this interval give EXACTLY the same information as the hypothesis test in Part A? EXPLAIN why - be very specific!
Car X Y
1 92 95
2 86 86
3 85 84
4 76 80
5 97 99
6 89 92
7 88 91
8 86 89
9 82 83
10 81 79
11 79 81
12 83 84
13 94 92
14 93 97
15 83 84
16 84 82

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach and construction of confidence interval is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.

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