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kevinzhu · 2021年02月07日

如何查表

  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.

不理解为何这道题目不需要5%/2而是直接选用5%来查表，跟前面的题目如何比较，

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1 个答案

星星_品职助教 · 2021年02月07日

同学你好，

通过题干的描述分析可得，这道题的备择假设是bj＜0.5。备择假设决定了拒绝域，所以这道题的拒绝域就在左侧，并且是一个单尾检验。

此时0.05 level of significance指的就是左侧拒绝域面积就是0.05或5%。因为这个时候已经不存在右尾了。

根据Exhibit 3，右侧面积为0.050时对应的关键值是1.645，所以根据对称性，左侧面积为0.05时的关键值即为-1.645

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如果这道题是双尾检验，例如备择假设是Ha：bj≠0，那么此时0.05 level of significance对应的关键值就是1.96了（因为两侧尾部面积总和是5%，单侧就是5%/2=2.5%）

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这道题是假设检验的问题，假设检验会出现单尾和双尾，取决于备择假设；这点和置信区间问题不同，置信区间（在数量里）一定是有两个尾巴。

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2023-04-27 00:12 2 · 回答

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