# Question

1. Test the null hypothesis at α = 0.05. 2. Later it was found that quite a few tires failed on the road. As a part of the investigation, the above hypothesis test is reviewed. Considering the high cost of type II error, the value of 5% for α is questioned. The response was that the cost of type I error is also high because the new method could save millions of dollars. What value for α would you say is appropriate? Will the null hypothesis be rejected at that α?

3. A review of the tests conducted on the samples reveals that 40 otherwise identical pairs of tires were randomly selected and used. The two tires in each pair underwent the two different methods, and all other steps in the manufacturing process were identically carried out on the two tires. By virtue of this fact, it is argued that a paired difference test is more appropriate. Conduct a paired difference test at α = 0.05.

4. The manufacturer moves to reduce the variance of the strength by improving the process. Will the reduction in the variance of the process increase or decrease the chances of type I and type II errors?

A tire manufacturing company invents a new, cheaper method for carrying out one of the steps in the manufacturing process. The company wants to test the new method before adopting it, because the method could alter the interply shear strength of the tires produced. To test the acceptability of the new method, the company formulates the null and alternative hypotheses as where μ1 is the population mean of the interply shear strength of the tires produced by the old method and μ2 that of the tires produced by the new method.

The evidence is gathered through a destructive test of 40 randomly selected tires from each method. Following are the data gathered:

H0: μ1 – μ2 ≤ 0

H1: μ1 – μ2 > 0

3. A review of the tests conducted on the samples reveals that 40 otherwise identical pairs of tires were randomly selected and used. The two tires in each pair underwent the two different methods, and all other steps in the manufacturing process were identically carried out on the two tires. By virtue of this fact, it is argued that a paired difference test is more appropriate. Conduct a paired difference test at α = 0.05.

4. The manufacturer moves to reduce the variance of the strength by improving the process. Will the reduction in the variance of the process increase or decrease the chances of type I and type II errors?

A tire manufacturing company invents a new, cheaper method for carrying out one of the steps in the manufacturing process. The company wants to test the new method before adopting it, because the method could alter the interply shear strength of the tires produced. To test the acceptability of the new method, the company formulates the null and alternative hypotheses as where μ1 is the population mean of the interply shear strength of the tires produced by the old method and μ2 that of the tires produced by the new method.

The evidence is gathered through a destructive test of 40 randomly selected tires from each method. Following are the data gathered:

H0: μ1 – μ2 ≤ 0

H1: μ1 – μ2 > 0

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