type 1 和type 2error

问题如下：

An oil industry analyst with a large international bank has constructed a sample of 1,000 individual firms on which she plans to perform statistical analyses. She considers either decreasing the level of significance used to test hypotheses from 5% to 1%, or removing 500 state-run firms from her sample. What impact will these changes have on the probability of making Type I and Type II errors?

选项：

Level of significance decrease Reduction in sample size

A.

P(Type I error) increases P(Type I error) increases

B.

P(Type I error) decreases P(Type II error) increases

C.

P(Type II error) increases P(Type I error) decreases

D.

P(Type II error) decreases P(Type II error) decreases

解释：

A Type I error is the error of rejecting a hypothesis when it is true. A Type II error is the error of accepting a false hypothesis.

A decrease in the level of significance decreases P(Type I error) but increases P(Type II error). Reducing the sample size increases P(Type II error).