Quality Improvement Partners (QIP) is a consulting firm that advises clients about sampling and statistical procedures that can be used to control their manufacturing processes. Your company has given QIP a sample of 800 observations taken during a time in which your process was operating satisfactorily.

The design specification indicates the mean measurement for the process should be 12. The sample standard deviation for these data was 0.21. With that much data, you can assume the population standard deviation is 0.21.

QIP has suggested that periodic random samples of size 30 be taken so you can monitor the process on an ongoing basis. By analyzing the new samples, you can quickly learn whether the process is operating satisfactorily or if it is operating differently than the expected mean. When the process is not operating satisfactorily, corrective action can be taken to attempt to eliminate the root cause(s) of the errors (assuming you know what they are). You will take corrective action whenever you reject the null hypothesis at the 0.01 significance level.

If you conduct a hypothesis test on one of the four samples provided to determine if the process is operating satisfactorily, it should be one sample z-test for the population mean (given the information provided in the Background information provided).

Null and alternative hypothesis =>Ho: ? = 12 and Ha: ? ? 12

Sample 1 Sample 2 Sample 3 Sample 4 12.03 12.1 11.85 11.64 11.94 12.01 12.16 12.39 11.92 11.99 11.91 11.65 12.13 12.2 12.12 12.11 12.09 12.16 11.61 11.9 11.93 12 12.21 12.22 12.21 12.28 11.56 11.88 12.32 12.39 11.95 12.03 11.93 12 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 12.2 11.77 11.84 12.12 11.79 12 12.07 11.6 12.3 12.04 12.11 11.95 12.27 11.98 12.05 11.96 12.29 12.3 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 12.3 12.37 11.88 12.23 12.15 12.22 11.93 12.25