One of the major U.S. tire makers wishes to review is warranty for their rainmak

Question

One of the major U.S. tire makers wishes to review is warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample 144 tires revealed that the mean number of miles is 45,000 miles with standard deviation of 15.000 miles. Test the hypothesis with a 0.05 significance level that the tire maker's claim is true. 1. What is H_0? _____ 2. What is H_1? 3. What is the decision rule? ______What is the calculated value of z? _____ What is the p-value for the test? ______is your decision? ______

Explanation / Answer

null hypothesis: mean =40000

alternate hypothesis: mean >40000

decision rule : reject Ho if test stat z>1.645

for std error=std deviation/(n)1/2 =1250

hence calculated z=(X-mean)/std deviation =(45000-40000)/1250=4

p value =0.00003

as p value is less then 0.05 level ; we reject null hypothesis and conclude that mean life is greater then 40000

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