For tests of hypotheses about μ, β decreases as the sample size increases if the level of significance stays the same.

Question

Quizplus · Accepted Answer

As the sample size increases, the standard error decreases, leading to a narrower distribution of sample means. This results in a larger t-value or z-value for a given level of significance and hence decreases the likelihood of committing a Type II error. Therefore, the power of the test increases and the probability of a Type II error (β) decreases.

For Tests of Hypotheses About μ, β Decreases as the Sample