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ruby5ltc · 2023年01月23日

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  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.

critical value为什么是负的1.645，而不是1.645？

如果是双尾检验，95%的置信区间，critical value是否等于1.96？

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2 个答案

星星_品职助教 · 2023年01月30日

​@ruby5ltc  逻辑为：因为是单尾检验，所以0.05 level of significance就对应单侧尾部面积5%。 又根据备择假设，可知此时拒绝域在左侧，所以关键值为 -1.645.

星星_品职助教 · 2023年01月28日

同学你好，

1）根据备择检验 Ha：bj＜0，本题的拒绝域在左侧，所以需要考虑的是左侧的critical value，也就是负值；

2）假设检验≠置信区间。如果是正态分布，95%置信区间的critical value等于±1.96；如果是正态分布下的双尾检验，且significance level=5%，则critical value同样等于±1.96

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2024-01-31 16:01 1 · 回答

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2023-04-27 00:12 2 · 回答

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