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Meeker (1987) reports the results of a life test on n = 100 b bearing tested for

ID: 3179177 • Letter: M

Question

Meeker (1987) reports the results of a life test on n = 100 b bearing tested for all 100 million of revolutions. Use the ball bearing life test data given below to answer following a. Compute a nonparametric estimate of the population fraction failing by 95 million cycles. b. Use the conservative (binomial based) interval to compute an approximate 90% confidence interval for population fraction failing by 95 million cycles c. Use the normal approximation method to compute an approximate 90% confidence interval for the population fraction failing by 95 million cycles. d. Comparing the intervals from part band c, . What do you conclude about the adequacy of the normal-approximation methods for these data?

Explanation / Answer

a. There are 17 out of 18 ball bearings failing by 95 m revolutions so fraction = 17/18 = 0.944

c. Normal approximation:

std deviation = sqrt(.94*(1-.94)) =0.2375

Std error = SD/sqrt(n) = 0.2375/10 = 0.0238

C.I. = .944 +-1.65* 0.0238

Lower limit = 0.905

upper limit = 0.983