To:| Peter Dalley|
From:| Harp Bhander|
Re:| Analysis Results|
Quality Associates, a consulting firm has been approached by a client to analyze their manufacturing process. The client came to Quality Associates with a sample of 800 observations that they had collected during times when the manufacturing process was running smoothly. The sample of 800 yielded a sample standard deviation of 0.21. Quality Associates suggested that the company periodically take a sample of 30 to monitor their process on an ongoing basis to quickly learn if process was operating at a satisfactory level, and if not it could quickly be adjusted. The specifications of the design calls for the mean of the process to be 12.
Sample size=30| Sample 1| Sample 2| Sample 3| Sample 4| Mean| 12.54| 12.04| 11.04| 12.05|
Min| 12.01| 11.62| 10.58| 11.64|
Max| 12.82| 12.48| 11.46| 12.54|
SD| 0.19| 0.18| 0.20| 0.25|
The Hypothesis test that will be conducted is as follows:
Ho: µ = 12
Ha: µ ≠12
Sample Number| Test Statistic| P Value| Do not Reject Ho| Reject Ho| 1| 14.11| 0.00| | X|
2| 1.08| 0.22| X| |
3| -25.05| 0.00| | X|
4| 1.33| 0.16| X| |
The preceding table shows us that we should not reject Ho for processes 2 and 4, while we should not accept Ho for processes 1 and 3. The results of our hypothesis test let us assume that processes 2 and 4 are equal to 12, meaning that these processes are operating smoothly while processes 1 and 3 do not satisfy our hypothesis test and are not equal to 12, letting us know that these processes need to be adjusted to meet the parameters that satisfy the hypothesis test. To ensure the validity of this test, and to make sure that our test statistics were relevant, an assessment of the relevance the population standard deviation needed to be conducted.
At the beginning of the report recall...