Quality Associates, Inc. is a consulting firm that advises its clients about sampling and statistical procedures that can be used to control manufacturing processes. In one case, a client provided Quality Associates with a sample of 800 observations that were taken during a time when the client's process was operating satisfactorily. The sample standard deviation for these data was .21, hence, the population standard deviation was assumed to be .21. 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 that the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows:
H0: = 12
Ha: /= 12
Corrective action will be taken when H0 is rejected. Samples collected during the first day of operation of the new statistical process-control procedure are in the file Quality.xls. The URL to this dataset is
A. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any should be taken,
B. Consider the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation seem reasonable?
The solution provides step by step method for the calculation of test statistic and p value. Formula for the calculation and Interpretations of the results are also included.