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 client's process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be known at 0.21. 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 would 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 by Quality Associates is stated below. H 0 ; μ = 12 H a ; μ ≠ 12 Corrective action will be taken anytime H0 is rejected.
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 client's process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be known at 0.21. 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 would 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 by Quality Associates is stated below.
H 0 ; μ = 12
H a ; μ ≠ 12
Corrective action will be taken anytime H0 is rejected.
The following samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the data set Quality.
Quality.xlsx
| Sample 1 | Sample 2 | Sample 3 | Sample 4 |
| 11.55 | 11.62 | 11.91 | 12.02 |
| 11.62 | 11.69 | 11.36 | 12.02 |
| 11.52 | 11.59 | 11.75 | 12.05 |
| 11.75 | 11.82 | 11.95 | 12.18 |
| 11.90 | 11.97 | 12.14 | 12.11 |
| 11.64 | 11.71 | 11.72 | 12.07 |
| 11.80 | 11.87 | 11.61 | 12.05 |
| 12.03 | 12.10 | 11.85 | 11.64 |
| 11.94 | 12.01 | 12.16 | 12.39 |
| 11.92 | 11.99 | 11.91 | 11.65 |
| 12.13 | 12.20 | 12.12 | 12.11 |
| 12.09 | 12.16 | 11.61 | 11.90 |
| 11.93 | 12.00 | 12.21 | 12.22 |
| 12.21 | 12.28 | 11.56 | 11.88 |
| 12.32 | 12.39 | 11.95 | 12.03 |
| 11.93 | 12.00 | 12.01 | 12.35 |
| 11.85 | 11.92 | 12.06 | 12.09 |
| 11.76 | 11.83 | 11.76 | 11.77 |
| 12.16 | 12.23 | 11.82 | 12.20 |
| 11.77 | 11.84 | 12.12 | 11.79 |
| 12.00 | 12.07 | 11.60 | 12.30 |
| 12.04 | 12.11 | 11.95 | 12.27 |
| 11.98 | 12.05 | 11.96 | 12.29 |
| 12.30 | 12.37 | 12.22 | 12.47 |
| 12.18 | 12.25 | 11.75 | 12.03 |
| 11.97 | 12.04 | 11.96 | 12.17 |
| 12.17 | 12.24 | 11.95 | 11.94 |
| 11.85 | 11.92 | 11.89 | 11.97 |
| 12.30 | 12.37 | 11.88 | 12.23 |
| 12.15 | 12.22 | 11.93 | 12.25 |
Download this dataset and write a managerial report addressing the following:
1. Conduct a hypothesis test for each sample at the 0.01 level of significance and report on what action, if any, should be taken. Make sure to provide the test-statistic and p-value for each sample.
2. Compute the standard deviation for each sample and comment on whether the assumed value of 0.21 appears to be reasonable.
3. Compute limits for the sample mean 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. These limits are referred to as upper and lower quality control limits. Comment as a manager on how these limits were determined and what the implications are of possibly changing the level of significance used to construct those limits.
Notes: Your report should address these issues as if you are an employee who is giving a report to your manager on your findings regarding the samples of data. Your report should have the following format and sections.
section 1. Introduction (purpose of report and summary of findings)
section 2. Summaries of your findings regarding the issues above
section 3. Recommendations to the manager on improving quality control, if it necessary. If not necessary, briefly justify why based on the data.
section 4. Any visual aids or summarization of the data and test-statistics that is helpful to the manager.
Upload your report here, preferably using Microsoft Word, standard text and font. There is no requirement on length -- the idea is that you are just simply informing your manager what your recommendations are based on the data and testing, and briefly justifying why.
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