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In the Analyze phase of the DMAIC approach, we shall test several hypotheses in order to determine the factors that the outputs (which need to be improved) depend on.
In this module, we review hypothesis testing concepts using Minitab, a popular statistical software tool for quality improvement. One can download a free trial version of Minitab and install it on his/her personal computer.
Review this tutorial on how to use Minitab to perform hypothesis testing.
Example One
The length of the shafts produced by a machine has historically been 20 mm with a standard deviation of 3 mm. The old machine has been replaced with a new one. The process owner wishes to check whether the new machine's performance is similar to that of the old one. He takes a sample of 40 shafts by the new machine and calculates the average length as 22 mm. Assume that the level of significance is 0.05.There is sufficient evidence to say that the new machine's performance is not similar to that of the old one.
Example Two
The length of the shafts produced by a machine has historically been 30 mm with a standard deviation of 5 mm. The old machine has been replaced with a new one. The process owner wishes to check whether the new machine's performance is similar to that of the old one. He takes a sample of 25 shafts by the new machine and calculates the average length as 31 mm and the standard deviation as 5 mm. Assume that the level of significance is 0.05.
There is insufficient evidence to say that the new machine's performance is not similar to that of the old one.
Verified Expert
This task provides a clear working example of one sample t test and one sample z test. when the sample size is large (n > 30) and the population standard deviation is known, then, we should perform one sample z test. On the other hand, when the sample size is small (n < 30) and the sample size is unknown, then we should perform one sample t test.
Solve Examples 1 through 5 using Minitab and interpret the output in each example to conclude whether the null hypothesis must be rejected.
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