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

Question

Mathematics

Gracie Mora

31 March, 12:17

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

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Isabel Krause · 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