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琳 · 2024年08月21日

如题

  1. CFA I
  2. Quantitative

NO.PZ2017092702000140

问题如下：

An investment consultant conducts two independent random samples of 5-year performance data for US and European absolute return hedge funds. Noting a 50 basis point return advantage for US managers, the consultant decides to test whether the two means are statistically different from one another at a 0.05 level of significance. The two populations are assumed to be normally distributed with unknown but equal variances. Results of the hypothesis test are contained in the tables below.

The results of the hypothesis test indicate that the:

选项：

A.

null hypothesis is not rejected.

B.

alternative hypothesis is statistically confirmed.

C.

difference in mean returns is statistically different from zero.

解释：

A is correct.

The t-statistic value of 0.4893 does not fall into the critical value rejection regions (≤ –1.984 or > 1.984). Instead it falls well within the acceptance region. Thus, H0 cannot be rejected; the result is not statistically significant at the 0.05 level.

t检验的拒绝原假设逻辑为：|test statistic|＞|critical value|，

根据这个原则，直接选择A，无法拒绝原假设。

麻烦老师讲解一下题干和表格，答案会选，题目考察的是什么意思不理解，谢谢

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1 个答案

品职助教_七七 · 2024年08月21日

嗨，爱思考的PZer你好：


这道题题干说的是根据抽出来的sample，US基金的return要高于欧洲基金50个bp（表格中的sample mean return 4.7和4.2），所以要检验一下这两个基金的平均收益是不是相等。此后通过表格给出了假设检验的一系列数据。

前面背景都不重要，最后问的就是根据表格去判断假设检验的结果是拒绝还是不拒绝。

由于没有其他条件，所以直接看表格中给了什么。看到分别给出了test statistic和critical value的值后就可以直接去做判断。判断原则为：

如果|test statistic|＞|critical value|，则拒绝原假设。

但由于判断结果是0.4983＜1.984，所以结论是不能拒绝原假设。故选择A。

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