This one is a bit more complicated. Because we can make an error in either direction, we need to divide our alpha level in half. So, even though we still have 5% error, half of it is in the upper, or right, tail of the distribution and half is in the lower, or left, tail of the distribution. This is what makes the test a two-tailed test. We now have Type II error in both alternative distributions. We still collect one sample and reject the null for that sample. Therefore, for any given hypothesis test, there is more possible Type II error and less statistical power in our test.
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