Question

1. 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)

Answer 1

Solution:

a) The null and alternative hypotheses are:

b) We have to use the z-test for a single proportion.

The test statistic is:

Where:

c. Since the p-value is greater than the significance level 0.05, we, therefore, fail to reject the null hypothesis.