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treepple · 2021年02月25日

请问这里为什么是单尾检验？

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

NO.PZ201512020300000303

问题如下：

3.The most appropriate null hypothesis and the most appropriate conclusion regarding Hansen’s belief about the magnitude of the initial return relative to that of the pre-offer price adjustment (reflected by the coefficient bj) are:

选项：

Null Hypothesis
Conclusion about bj(0.05 Level of Significance)
A.
H0: bj=0.5
Reject H0
B.
H0: bj≥0.5
Fail to reject H0
C.
H0: bj≥0.5
Reject H0

解释：

C is correct.

To test Hansen’s belief about the direction and magnitude of the initial return, the test should be a one-tailed test. The alternative hypothesis is H1: bj<0.5b_j<0.5, and the null hypothesis is H0: bj≥0.5b_j\geq0.5. The correct test statistic is: t = (0.435-0.50)/0.0202 = -3.22, and the critical value of the t-statistic for a one-tailed test at the 0.05 level is -1.645. The test statistic is significant, and the null hypothesis can be rejected at the 0.05 level of significance.

是因为系数大于零所以是单尾检验吗？

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星星_品职助教 · 2021年02月26日

同学你好，

单/双尾检验要看备择假设。

以本题为例，原假设是H0: bj≥0.5，所以备择假设即为Ha: bj＜0.5。这个备择假设说明：

①单尾检验；②拒绝域在左侧单尾。

理解角度为：假设的是这个数字大于0.5，但随便抽一个数字，如果发现远“小于0.5”，那么原始的假设就是错的。这个“小于0.5”对应的就是在0.5左侧。因为只有“小于”这一种情况，就是单尾。

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

对比一下，如果原假设是H0: bj=0.5，备择假设即为Ha: bj≠0.5。这个备择假设说明：

①双尾检验；②拒绝域在两端。

理解角度为：假设的是这个数字等于0.5，所以“不等于0.5”就有两种情况，一种是远大于0.5，一种是远小于0.5。所以拒绝域在两端都有。

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