For a fixed sample size n, as the probability of a Type II error $\beta$ decreases, the probability of a Type I error $\alpha$ increases.

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Quizplus · Accepted Answer

This is known as the "power vs. type I error trade-off." As one decreases, the other tends to increase. This is because as you decrease the probability of a Type II error, you are increasing the probability of correctly rejecting a false null hypothesis, which means you are more likely to reject a true null hypothesis (i.e. make a Type I error).

For a Fixed Sample Size N, as the Probability of a Type