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CY · 2021年05月01日

可以请助教解释一下这个 not equal to 类型题嘛

  1. CFA I
  2. Quantitative

NO.PZ2018062016000124

问题如下：

Which of the following descriptions on a two-tailed hypothesis test is least correct?

选项：

A.

A two-tailed test is less directive than a one-tailed test. 

B.

The alternative hypotheses of one-tailed tests has less impacts on the researcher's beliefs than the alternative hypotheses of two-tailed tests. 

C.

Under the same significance level, the absolute value of two-tailed test's rejection points is larger than the one of one-tailed test.

解释：

B is correct. A two-tailed test is a “not equal to” alternative hypothesis, while a one-tailed test is a “greater than” or “less than” alternative hypothesis. “greater than” or “less than” alternative hypotheses reflect the beliefs of the researcher more strongly than a "not equal to" alternative hypothesis.

这个题错了两次了，但是搞不懂题目问的和答案的逻辑～


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星星_品职助教 · 2021年05月01日

同学你好，

无论是 “not equal to” ，“greater than” 还是 “less than” 描述的都是备择假设（alternative hypothesis）。

如果原假设是例如假设均值等于一个确定的数，例如H0：μ=0，则备择假设就是Ha：μ≠0，这个不等于0的意思就是 “not equal to 0”。由于不等于0分为大于0和小于0这两种情况，拒绝域同时在左尾和右尾，所以就是双尾检验（a two-tailed test）

但如果原假设是假设均值大于等于一个数，例如H0：μ≥0，则备择假设就是Ha：μ＜0，这个小于0的意思就是“less than” 。此时拒绝域仅在左尾，所以就是单尾检验（a one-tailed test）

同理，“greater than”的情况就是反过来。

这里有一个小技巧，就是“等号”只会在原假设里出现，备择假设里不出现“=”，“≥”，“≤”。掌握这个技巧，选择会更快。

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如果备择假设是“not equal to 0”，说明研究者也不知道到底应该是大于0还是小于0，没有一个方向性，或者说对于和0的关系究竟如何信心不足。相反，如果备择假设是确定的大于0或者小于0，则说明研究者对于μ和0的关系有一个确定性的方向性，信心更足。所以A选项本身的描述是正确的，同时B选项描述错误。由于题目要选的是“ least correct”，直接选择B选项即可。

----------------

如果题目中出现类似C选项的这种描述，最好的办法就是直接用背过的值做一个例子来判断。

正态分布下，95%的单尾检验对应关键值（rejection point）的绝对值为1.645；而95%的双尾检验对应关键值的绝对值为1.96.

C选项的意思是双尾（ two-tailed）检验对应的关键值的绝对值要比单尾检验（one-tailed hypothesis test）的大，由于1.96确实大于1.65，所以C选项的描述是正确的，同样不能选。

考试时遇到类似的题目也直接用个例子迅速判断即可。



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