Case Study # 1: Quality Associates, Inc.
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: μ = 12
Ha: μ ≠ 12
Corrective action will be taken any time H0 is rejected.
The following samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. The data file containing samples is available as an excel attachment for easy upload into Mintab.
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 x̄ 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 the x̄ exceeds the upper limit or if x̄ 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 implication of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?