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IanZQ · 2022年07月03日

如何判断是否在拒绝域中？

  1. CFA II
  2. Quantitative

NO.PZ2015120204000015

问题如下：

Based on past research, Hansen selects the following independent variables to predict IPO initial returns:

Underwriter rank = 1–10, where 10 is highest rank

Pre-offer price adjustment (Expressed as a decimal) = (Offer price – Initial filing price)/Initial filing price

Offer size ($ millions) = Shares sold × Offer price

Fraction retained (Expressed as a decimal) = Fraction of total company shares retained by insiders

He also believes that for each 1 percent increase in pre-offer price adjustment, the initial return will increase by less than 0.5 percent, holding other variables constant. Hansen wishes to test this hypothesis at the 0.05 level of significance.

Hansen collects a sample of 1,725 recent IPOs for his regression model.

\Hansen’s Regression Results Dependent Variable: IPO Initial Return (Expressed in Decimal Form, i.e., 1% = 0.01)

Selected Values for the t-Distribution (df = ∞)

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.

C 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.

1） Ha>0.5, H0<=0.5 ，理解没问题；

2） t = (0.435-0.50)/0.0202 = -3.2，理解没问题；

3） 查表，T， 给的是RIGH TAIL是单尾，所以1.645转成 LEFT -1.64，这也理解没问题。

接下来怎么判断-3.2和-1.64，是否落在拒绝域的问题就有点不清晰了，希望老师能从基础出发，给一套逻辑便于判断。我记得课上何老师说“拒绝域跟备择假设”，这个怎么理解？

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1 个答案

星星_品职助教 · 2022年07月03日

同学你好，

拒绝原假设的逻辑是：如果|test statistic|＞|critical value|，则拒绝原假设。

本题|-3.22|＞|1.645|，直接就可以得出拒绝原假设的结论。

-------

备择假设决定了拒绝域的位置，本题备择假设应为Ha：bj＜0.5（根据“想拒绝的放在原假设，相信的放在备择假设，本题Hansen相信的是the initial return will increase by less than 0.5 percent”），

通过这个备择假设，可以得到拒绝域在左尾。

本题的考点和拒绝域的位置无关，可以在涉及到的题目下具体就细节提问。

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