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 that we analyzed the sample of 800 observations to compute a population standard deviation of 0. 21.
To further analyze our results and limit the potential for error, it was felt that the assumption that a 0. 21 standard deviation for the population must be reviewed to ensure it is applicable to our new sample data. The individual samples provided standard deviations of 0. 9, 0.
18, 0. 20, and 0. 25 for samples 1-4 respectively. To conclude if the standard deviations of our samples were still within a limit to consider a sigma of 0. 21 to be considered relevant the mean standard deviation of the samples was taken, the resulting value for the mean of our samples was approximately 0.
21, allowing us to consider our population standard deviation to be reasonable. Along with testing the population standard deviation to test its validity for the samples analyzed, upper and lower control limits were established.Establishing control limits gives us parameters within which we can operate in the case of a new sample mean. Computing our margin of error we have determined that as long as a process is ±0. 10 of 12 we can consider a process to be operating satisfactorily.
If however a new sample mean falls below 11. 90 or above 12. 10 the process must be stopped and corrective action must be taken to bring the sample mean back within the acceptable limits. To have the highest level of confidence in the findings, this hypothesis test was conducted at a . 1 level of significance. Had we conducted our study with an alpha of .
05 or . 10 we would have left ourselves more likely to falsely reject a null hypothesis, leading us to commit a type I error. The results of the test are presented to you with the highest level of assurance regarding the accuracy of our findings. Any questions or concerns regarding the findings enclosed within this analysis can be addressed directly to me at (250)-123-9876 ext. 994
