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Captain America · 2022年09月02日

请解释一下C选项

  1. CFA I
  2. Quantitative

NO.PZ2017092702000123

问题如下：

A hypothesis test for a normally-distributed population at a 0.05 significance level implies a:

选项：

A.

95% probability of rejecting a true null hypothesis.

B.

95% probability of a Type I error for a two-tailed test.

C.

5% rejection region in a tail of the distribution for a one-tailed test.

解释：

C is correct.

For a one-tailed hypothesis test, there is a 5% rejection region in one tail of the distribution.

对于单尾的检验（for a one-tailed test），单侧拒绝域是5%。

同样都是95%，单尾是0.05等同于双尾的0.025吗？

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星星_品职助教 · 2022年09月03日

同学你好，

不等于，0.05和0.025都是面积的概念，两者不相等。

当significance level=5%，且为单尾检验的时候，单尾的拒绝域面积为5%。

当significance level=10%，且为双尾检验的时候，双尾拒绝域的总面积为10%，此时单尾的拒绝域也为5%。

上述两种情况的关键值均为1.645（假设为正态分布）

当significance level=5%，且为双尾检验的时候，双尾拒绝域总面积为5%，此时单尾的拒绝域为2.5%，对应关键值为1.96（假设正态分布）

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