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circle · 2024年03月07日

关于双尾和单尾

NO.PZ2018062016000124

问题如下:

Which of the following descriptions on a two-tailed hypothesis test is least correct?

选项:

A.

A two-tailed test is less directive than a one-tailed test. 

B.

The alternative hypotheses of one-tailed tests has less impacts on the researcher's beliefs than the alternative hypotheses of two-tailed tests. 

C.

Under the same significance level, the absolute value of two-tailed test's rejection points is larger than the one of one-tailed test.

解释:

B is correct. A two-tailed test is a “not equal to” alternative hypothesis, while a one-tailed test is a “greater than” or “less than” alternative hypothesis. “greater than” or “less than” alternative hypotheses reflect the beliefs of the researcher more strongly than a "not equal to" alternative hypothesis.

老师,我这样理解是对的吗:双尾显著水平5%,置信区间95%;单位显著水平5%,置信区间也应该是95%是吧,但是看其他同学提问下如果解答,感觉是也算上一侧的5%,然后90%得出关键值+-1.65.

感觉自己没太弄懂,谢谢!



1 个答案

品职助教_七七 · 2024年03月07日

嗨,努力学习的PZer你好:


对于非VaR的情况,置信区间都是双尾,所以置信区间95%指的就是中间部分95%,两侧尾部各2.5%。数量中说到置信区间,基本都是这种情况。

只有对于VaR的情况,才会出现单尾的置信区间。VaR主要是组合中的内容,如果题目没有强调这是VaR的背景,则不需要考虑这类情况。


在非VaR的常规情况下,正态分布下95%的置信区间的单侧尾部面积为2.5%,关键值为±1.96。90%的置信区间的单侧尾部面积为5%,关键值为±1.65;

但在VaR的情况下,5%的VaR相当于左侧单侧尾部面积就是5%,所以关键值就和非VaR情况下的90%置信区间一样了,也就是-1.65。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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