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