Statistical Significance is associated with inferential statististics, and is defined as being able to see evidence of difference at the accepted risk for a given hypothesis test. In the case of the prior message, with and alpha = .05, that would mean that you can see the difference and be 95% confident of your decision. While the 5% risk level is often used by default, risk levels should reflect the criticality of the process test and your willingness to decide something is defferent when it is really not different (a cost to your company). With an XBar control chart we generally test to slightly over 99% confidence.
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