Statisitical tables also can be confusing. The figure shows a chi square distribution with 6 degrees of freedom. 12.59 is the 95th percentile of the distribution. It is the integral of the distribution from 0 to 12.59, and 95 percent of the area under the curve is to the left of 12.59. Power A test's power improves with sample size.
Tests also become more powerful as the situation gets worse.
As the wolf gets closer, the shepherd is more likely to see it. It is the reciprocal of the power. Some people say that a control chart is not a hypothesis test. We can, therefore, characterize a nonnormal process and set appropriate control limits for it. In any event, when we start talking about average run lengths, and a control chart's false alarm risks, this implies a hypothesis test.