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Ella · 2024年01月08日

这题n应该取36*2=72吧

NO.PZ2017092702000162

问题如下:

The following table shows the sample correlations between the monthly returns for four different mutual funds and the S&P 500. The correlations are based on 36 monthly observations. The funds are as follows:


Test the null hypothesis that each of these correlations, individually, is equal to zero against the alternative hypothesis that it is not equal to zero. Use a 5 percent significance level.





选项:

解释:

The critical t-value for n − 2 = 34 df, using a 5 percent significance level and a two-tailed test, is 2.032. First, take the smallest correlation in the table, the correlation between Fund 3 and Fund 4, and see if it is significantly different from zero. Accoding to the formula of correlaion t-test, its calculated t-value is t=1.903. This correlation is not significantly different from zero. If we take the next lowest correlation, between Fund 2 and Fund 3, this correlation of 0.4156 has a calculated t-value of 2.664. So this correlation is significantly different from zero at the 5 percent level of significance. All of the other correlations in the table (besides the 0.3102) are greater than 0.4156, so they too are significantly different from zero.

不可能是5种一共36个观察值,这也无法整除,所以肯定是每种36个观察值,那每个correlation都有36*2=72个观察值参与计算,所以n应该等于72

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品职助教_七七 · 2024年01月09日

嗨,从没放弃的小努力你好:


“The correlations are based on 36 monthly observations”的理解应为:

每个月,所有的Fund1-Fund4和S&P 500都会有一个return,连续观察36个月,得到上述4只基金和S&P 500各自的36个return。据此算出这5个主体之间两两的sample correlation。

如Fund 3有36个return,Fund 4也有对应时间段的36个return,由此就可以算出Fund 3和Fund 4之间的correlation。题目表格直接给出了这个数字应为0.3102.

由于观察值有36个,所以n为36。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Ella · 2024年01月09日

那这道题No.PZ2023061301000026 (选择题)里的248为什么不要除2后再减2啊

品职助教_七七 · 2024年01月09日

嗨,爱思考的PZer你好:


@Ella

这道题n的原理和本题是一样的。两个变量是Stellar return和CPIENG。248个观察值相当于有248个stella的return和与之对应的248个CPIENG,所以n就是248。

根据这248组数据,可以算出Stellar return和CPIENG的correlation。

所有的题目都没有除以2算n的这种考法。n一般都是直接给出的observations的数量。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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