For a given sample size,the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

The probability of committing a Type I error (rejecting a true null hypothesis) and the probability of committing a Type II error (failing to reject a false null hypothesis) are inversely related. As the probability of committing a Type I error decreases, the probability of committing a Type II error increases because the null hypothesis is less likely to be rejected even when it is false. This tradeoff between Type I and Type II errors is known as the "power" of a statistical test, and it is important to balance these two types of errors based on the goals and context of the study.