Case analysis

Case Analysis 2

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical

procedures that can be used to control their manufacturing process. In one particular application,

a client gave Quality Associates a sample of 800 observations taken during a time in which that

client’s process was operating satisfactorily. The sample standard deviation for these data was

0.218; hence. With so much data, the population standard deviation was assumed to be 0.218.

Quality Associates then suggested that random samples of size 30 be taken periodically to

monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly

learn whether the process was operating satisfactorily. When the process was not operating

satisfactorily, corrective action could be taken to eliminate the problem. The design specification

indicated the mean for the process should be 12. The hypothesis test suggested by Quality

Associates follows.

𝐻0: 𝜇 = 12

𝐻𝐴: 𝜇 ≠ 12

Corrective action will be taken anytime 𝐻0 is rejected. The following samples were collected at

hourly intervals during the first day of operation of the new statistical process control procedure.

These data are available in the data set “Quality”.

Questions)

1. Conduct a hypothesis test for each sample at the 0.05 level of significance and determine

what action, if any, should be taken. Provide the test statistic and p-value for each test.

Answer this using at least 150 words. (45 points)

2. Compute the standard deviation for each of the four samples. Does the assumption of

0.218 for the population standard deviation appear reasonable? Answer this using at

least 100 words. (15 points)

3. Discuss the implications of changing the level of significance to a larger value. What

mistake or error could increase if the level of significance is increased? Answer this

using at least 100 words. (15 points)