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Helen 🎈 · 2022年12月31日

老师能解释下第一段吗

NO.PZ2021071601000004

问题如下:

The sample correlation between the GBP monthly returns to Japanese yen and Canadian dollar is 0.5132 for the period from January 2011 through December 2017.

Can we reject a null hypothesis that the underlying or population correlation equals 0 at the 0.05 level of significance?

At the 0.05 significance level, the critical level for this test statistic is 1.99 (n = 84, degrees of freedom = 82

选项:

A.Yes.

B.No.

C.Neither.

解释:

A is correct.

With 84 months from January 2011 through December 2017, we use the following statistic:


When the test statistic is either larger than 1.99 or smaller than −1.99, we can reject the hypothesis that the correlation in the population is 0. The test statistic is 5.4146, so we can reject the null hypothesis.

还是不太能够深刻理解correlation 的意思,感觉在考试中,会不知道这道题该用啥公式。

1 个答案

星星_品职助教 · 2023年01月01日

同学你好,

本题问能否拒绝correlation等于0的原假设。所以是检验correlation的问题。需要根据correlation的t检验的公式,计算出correlation的test statistic,然后和critical value作对比,判断能否拒绝原假设。

根据公式:

其中r为sample correlation,根据题干第一段可知,r=0.5132。再代入已知的n-2=82,求得此时test statistic=5.4146.

再用test statistic和已知的critical value=1.99对比,根据test statistic>critical value,得出拒绝原假设的结论.

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