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 game
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 .21; hence, with so much
data, 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 the mean for the process should be 12. The
hypothesis test suggested Quality Associates follows.
H0: μ=12
H1: μ≠12
Corrective action will be take any time H0 is rejected.
Four samples were collected at hourly intervals during the first day of operation of the new statistical
process control procedure. The data are available in the data set Quality.xls.
Managerial Report:
- 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.
- Compute the standard deviation for each of the four samples. Does the assumption of .21 for
the population standard deviation appear reasonable?
- Compute limits for the sample mean X around μ=12 such that, as long as a new sample mean is
within those limits, the process will be considered to be operating satisfactorily. If X exceeds the
upper limit or if X is below the lower limit, corrective action will be taken. These limits are
referred to as upper and lower control limits for quality control purposes.
- Discuss the implications of changing the level of significance to a larger value. What mistakes or
error could increase if the level of significance in increased?