A tire manufacturing company is reviewing the warranty for their rainmaker tire.

Question

A tire manufacturing company is reviewing the warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. a. assume you are trying to determine if the tire lasts more than 40,000 miles. Determine the appropriate hypothesis test. b. determine the value of the test statistic c. determine the critical z or t value using a level of significance of 5% d. determine the p-value e. state you conclusion: reject HO or do not reject f. what is the probability of making a type I error?

Explanation / Answer

(a) The appropriate test is a single sample z- test for a population mean

(b)

Data:    

n = 49   

= 40000   

s = 15000   

x-bar = 45000   

Hypotheses:    

Ho: 40000   

Ha: > 40000   

Test Statistic:

SE = s/n = 15000/49 = 2142.857143

z = (x-bar - )/SE = (45000 - 40000)/2142.85714285714 = 2.333333333

(c) Decision Rule:

= 0.05   

Critical z- score = 1.644853627   

Reject Ho if z > 1.644853627

(d) p- value = 0.009815329   

(e) Decision (in terms of the hypotheses):    

Since 2.333333333 > 1.644853627 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that > 40000

(f) 0.0098

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