# Power of Hypothesis Tests

We make a Type I error when we incorrectly reject the null hypothesis when we shouldn't.
The probability of making a Type I error is α. We can control this by choosing a
higher or lower rejection criteria. For each α level, there is an associated z*
that corresponds to the probability of the normal probability density function.
We make a Type II error when we fail to reject the null hypothesis when we should.
The probability of making a Type II error is β. We have less control of this,
but there are a few factors that effect it. Incresing the sample size helps narrow the
distribution if the sample mean, and just how far the actual poplation mean is from our
null hypothesis effects this as well.

The power of a Hypothesis test is the probability of NOT making a Type II error, that
is, 1-β.

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