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Helen 🎈 · 2022年12月27日

significance level

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。

老师,请问下这道题significance level是0.05那就是1.96

是不是1.984也可以跟1.96比较,结论是不能拒绝。

1 个答案

星星_品职助教 · 2022年12月27日

同学你好,

1)本题是t检验,1.96是正态分布下的关键值,在本题中不适用;

2)1.984和1.96都是关键值,无法比较;

3)关键值和test statistic进行比较。如果是正态分布,则为1.96和0.4893比较。

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