Final answer:
True. Six Sigma quality aims for a small number of defects by ensuring the process mean is six standard deviations from the nearest specification limit, which is rooted in the concept of a normal distribution and the Empirical Rule.
Step-by-step explanation:
The statement that 'Six Sigma quality means that the difference between the upper and lower tolerance levels is six standard deviations wide' is True. This concept is a crucial part of quality management and process improvement strategies in businesses and engineering. Six Sigma aims for a process to be well-controlled, with minimal variation, which is defined as fewer than 3.4 defects per million opportunities.
When we say a process is Six Sigma, we imply that there are six standard deviations between the mean of the process and the nearest specification limit. This ensures that even if there is a slight shift in the process mean over time, the likelihood of producing a defect is extremely low.
To draw this back to statistical principles, the Empirical Rule, or 68-95-99.7 rule, tells us that for a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three. Six Sigma performs even better by ensuring the process mean is six standard deviations from the nearest specification limit.
In the context of hypothesis testing, as in the provided example, rejecting the null hypothesis when the p-value is less than the significance level (alpha) is consistent with the Six Sigma methodology, which seeks to minimize Type I and Type II errors in decision-making.