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台风来了 · 2023年08月02日

关于t统计量的单尾检验。

NO.PZ2023040502000010

问题如下:

Hansen 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.


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:

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: , and the null hypothesis is H0: .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.

老师,您好!


关于t统计量的单尾检验,如果原假设是>=某个值,当p-value < critical value,即本题中-3.22 < -1.645时,则拒绝原假设。

反之,如果原假设是<=某个值,当p-value > critical value,则拒绝原假设。是这样吗?谢谢!

2 个答案

星星_品职助教 · 2023年08月07日

@台风来了 是的

星星_品职助教 · 2023年08月03日

同学你好,

本题不涉及p-value,-3.22是test statistic。

拒绝原假设的原则为:|test statistic|>|critical value|,则拒绝。

本题拒绝原假设的原因即为|-3.22|>|-1.645|,和原假设的方向无关。

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