Question

6. (A) The information obtained from a random sample of 1,600 users of the Arctic Power Tires yielded a mean useful life of 251,000kms and a standard deviation of 30,000kms. (a) Test the hypothesis that the mean lifetime L of this make of tire is not significantly different from 250,000kms. Let o = 0.05. Assume that the useful life L is a normally distributed random variable. (b) The following is an interesting and useful way of finding an approximate (1-—o)100% confidence interval of the standard deviation o when the sample is large: Usc this result (i) to find a 95% confidence interval of the variance of the probability distribution of L and (ii) to test the hypothesis at the o = 0.05 level that the true standard deviation o is not significantly different from 25,000kms. 6. (B) A nation wide survey carried out on behalf of the Concerned Consumers Association revealed that 1,950 customers out of a random sample of 2,200 were satisfied with the quality of their DeliMark cell phone. (a) Test the hypothesis that the proportion of customers who are satisfied with the quality of their DeliMark cell phone is not significantly different from 0.90 Let o = 0.05. (b) How large should the sample be if we wish to know the true proportion of satisfied customers with an error of 0.01 and 99% confidence?

Answer 1