Question

A computer manufacturer is testing a batch of processors. They place a simple random sample of processors from the batch under a stress test and record the number of failures, their guidelines specify the percentage of failures should be under 4%. Of the 300 processors tested, there were 54 failures.

a. State the hypotheses for the test. Assume the manufacturer wants to assume there is a problem with a batch, that is, they will only accept that there are fewer than 4% failures in the population if they have evidence for it.

b. Calculate the test statistic and p-value. Your test statistic should be either a z-value or a t-value, whichever is appropriate for the problem

Answer 1

given data are calculations :-

sample size (n) = 300

sample proportion () = 54/300 = 0.58

a).hypothesis:-

the claim is the alternative hypothesis.

b). here, we will do 1 sample proportion Z test for mean.

the test statistic be:-

p value :-

decision:-

p value = 1 >0.05 (alpha)

so, we fail to reject the null hypothesis and conclude that there are no evidence to support that there are fewer than 4% failures in the population...so, they will not accept the lot.

***in case of doubt, comment below. And if u liked the solution, please like.