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remoo · 2019年11月15日

问一道题:NO.PZ2018062001000014

问题如下:

All else equal, a larger significant level indicates:

选项:

A.

A higher probability of type I error and type II error.

B.

A higher probability of type I error and lower probability of type II error.

C.

A lower probability of type I error and higher probability of type II error.

解释:

B is correct.

The significant level of a test is the probability of a Type I error. Therefore a larger significant level means a higher probability of Type I error.

Type II error occurs when we fail to reject a false null hypothesis. It will be smaller if significant level of a test is larger, all else equal.

significance level 越大说明 α 越大,在其他相等的情况下,不就意味着x-μ/x/根号下n,n变大了? n变大了,不是typeI 和type II 都变下?

1 个答案

星星_品职助教 · 2019年11月15日

同学你好,

这道题的all else equal的意思里面已经包含了n不变。其实如果刻意说了n变化,都是默认n不变的。解题思路建议是:significance level变大也就是α变大,α就是第一类错误,所以第一类错误上升。由于n不变的前提下,两类错误之间有此消彼长的关系,所以第二类错误下降。

两类错误同时下降的题型是会专门说n上升了,然后两类错误应该怎么变。加油



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