Is the mean lifetime of a particular type oftruck engine greater than 220,000 mi

Question

Is the mean lifetime of a particular type oftruck engine greater than 220,000 miles? To test this claim,a sample of 23 engines is measured, yieldingan average of 226,450 miles and a standard deviation of11,500 miles. Use a significance level of0.01. Use a hypothesis test to test the given claim for a normalpopulation. A)Reject the null hypothesis of m=220,000 with a P-value between .01 and .025. There issufficient evidence that the engines last longer than 220,000miles. B) Fail toreject the null hypothesis of m=220,000 with aP-value of greater than .10. There is not sufficientevidence thatthe engines last longer than 220,000miles. C) Reject thenull hypothesis of m=220,000 with aP-value between .005 and .01. There is sufficient evidence that theengines last longer than 220,000miles. D) Fail to reject the nullhypothesis with a P-value between .05 and .10.There is notsufficient evidence that the engines last longer than 220,000miles. E) None of the answers above iscompletelycorrect. Is the mean lifetime of a particular type oftruck engine greater than 220,000 miles? To test this claim,a sample of 23 engines is measured, yieldingan average of 226,450 miles and a standard deviation of11,500 miles. Use a significance level of0.01. Use a hypothesis test to test the given claim for a normalpopulation. A)Reject the null hypothesis of m=220,000 with a P-value between .01 and .025. There issufficient evidence that the engines last longer than 220,000miles. B) Fail toreject the null hypothesis of m=220,000 with aP-value of greater than .10. There is not sufficientevidence thatthe engines last longer than 220,000miles. C) Reject thenull hypothesis of m=220,000 with aP-value between .005 and .01. There is sufficient evidence that theengines last longer than 220,000miles. D) Fail to reject the nullhypothesis with a P-value between .05 and .10.There is notsufficient evidence that the engines last longer than 220,000miles. E) None of the answers above iscompletelycorrect.

Explanation / Answer

C) Minitab Outuput One-Sample T Test of mu = 220000 vs > 220000                               99%                             Lower N    Mean StDev SEMean   Bound    T      P 23 226450 11500     2398 220435 2.69 0.007 We can get the P-value=0.007. So the correct answer is C. Reject the null hypothesis of m=22000. There is sufficient evidencethat the engines last longer than 220000 miles.

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