Question

A special industrial battery must have a life of at least 400 hours. A hypothesis test is to be conducted with a 0.02 level of significance. If the batteries from a particular production run have an actual mean use life of 385 hours, the production manager wants a sampling procedure that only 10% of the time would show erroneously that the batch is acceptable. What sample size is recommended for the hypothesis test

Answer 1

Margin of error E = Z(alpha/2)*(sigma/sqrt(n))

From this equation we get n as

n = (z*sigma/E)^2

alpha= 0.02

from the standard normal table value we get

z(alpha/2) = 2.33

sigma = 30

E= 0.1

Therefore n =(2.33*30/0.1)^2

=488601

sample size n =488601