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. (2 points)

(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. (6 points)

(c) Reach your conclusion for the test at the 0.05 significance level. (2 points)

(d) One of the engineers wants to change the test to be at the 0.01 significance level. What would be the effect of doing so? (Answer this question generally, not just in the context of this particular problem.) (3 points)

Answer 1

a. Here claim is that there are fewer than 4% failures in the population if they have evidence for it.

As null hypothesis always have equality sign so hypothesis is

vs

b.

Test statistics is

So P value is

c. As P value is greater than alpha=0.05, we fail to reject the null hypothesis

d. As P value is greater than alpha=0.01, so decision will remain the same we will fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that p<0.04