In a manufacturing process,we are interested in measuring the average length of a certain type of bolt.Based on a preliminary sample of 9 bolts,the sample standard deviation is .3 inches.How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the true mean bolt length?
A)865
B)80
C)1470
D)3989
E)1197

Question

Quizplus · Accepted Answer

We can use the formula n = (z*sigma/E)^2, where n is the sample size, z is the z-score corresponding to the desired level of confidence (95% or 1.96), sigma is the population standard deviation (unknown), and E is the maximum error allowed for the sample mean (0.02 inches).
Substituting the given values, we have n = (1.96*0.3/0.02)^2 = 1197, rounded up to the nearest integer.
Therefore, the best choice is E, with a sample size of 1197 bolts.

In a Manufacturing Process,we Are Interested in Measuring the Average