A corporation makes CV joints for automobiles. An integral part of CV joints is the bearings that allow the joints to rotate differentially. One application utilizes six bearings in a CV joint that have an average diameter of 2.5 centimeters. The consistency of the diameters is vital to the operation of the joint. The specifications require that the variance of these diameters be no more than 0.0015 centimeters squared. The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are obtained every day. One of these subsamples produced bearings that had a variance of 0.00317 centimeters squared.
a. Calculate the probability that a subsample of size 10 would produce a sample variance that would be at least 0.00317 centimeters squared if the population variance was 0.0015 centimeters squared.
b. On the basis of your calculation in part a, conduct a hypothesis test to determine if the quality control team should advise management to stop production and search for causes of the inconsistency of the bearing diameters. Use a significance level of 0.05.