# Standard Deviation

10.21 An automobile company thinks that with new designs, it scars will last longer before having a problem. For this reason the company wishes to extend the warranty that comes with the vehicle in hopes of attracting more customers. Before making this change the idea is tested. Prior to the design changes, the cars lasted on the average 43 months before having a major problem. A sample consisting of 50 cars was tested. The cars lasted an average of 44 months before having a major problem. The standard deviation is 2 months.

a. Set up the null and alternative hypotheses to test if average time before having a major problem is longer than 43 months

b. Test your hypotheses using alpha = 0.05

c. Find the p value

d. Based on the p value, what can you conclude about the average time before having a major problem?

#### Solution Preview

Solution. Denote the warranty by X. Then X is a random variable. And we asuume that X follows the normal distribution, X~N(a,b^2), where a is the mean and b is the standard deviation.

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<br>Define the hypothesis.

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<br>H0: a=43,

<br>H1: a is not equal 43.

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<br>Let us consider the statistic T=(Xbar-a)*sqrt(n)/SX, where Xbar is the mean of the sample , ie., ...

#### Solution Summary

10.21 An automobile company thinks that with new designs, it scars will last longer before having a problem. For this reason the company wishes to extend the warranty that comes with the vehicle in hopes of attracting more customers. Before making this change the idea is tested. Prior to the design changes, the cars lasted on the average 43 months before having a major problem. A sample consisting of 50 cars was tested. The cars lasted an average of 44 months before having a major problem. The standard deviation is 2 months.

a. Set up the null and alternative hypotheses to test if average time before having a major problem is longer than 43 months

b. Test your hypotheses using alpha = 0.05

c. Find the p value

d. Based on the p value, what can you conclude about the average time before having a major problem?