Quality associates Inc. a consulting firm advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application a client gave quality associates a sample of 800 observations taken during a time in which that clients process was operating satisfactorily. The sample standard deviation for these data was .21. hence, with so much data the population standard deviation was assumed to be 0.21. quality associates then suggested the 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 the corrective action could be taken to eliminate the problem. The design specification indicated the mean for the process should be 12. The hypothesis tests suggested by the quality associates as follows:
Corrective actions will be taken anytime H0 is rejected.
The samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in another excel attachment.
1, Conduct a hypothesis test for each sample at the .01 level of significance and determine what action if any, should be taken. Provide the test statistic and p-value for each test.
2, compute standard deviation for each of the four samples. Does the assumption of 0.21 for the population standard deviation appear reasonable?