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小悟空 · 2020年06月02日

问一道题：NO.PZ2018062016000140

  1. CFA I
  2. Quantitative

问题如下：

During the table below, the mean monthly return of X Index in the first five years have been different than the mean return in the second five years.

Let the μ1 stand for the population mean return for the year1 through year 5 and μ2 stand for the population mean return for the year 6 through year 10, the following hypothese: H0: μ1 – μ2 = 0 versus Ha: μ1 – μ2 ≠ 0

Assume that the significant level is 0.05

Which of the following options is most accurate?

选项：

A.

The null hypothesis will be rejected if t<-1.98 or t>1.98.

B.

The t-test has 119 degrees of freedom.

C.

The rejection points are ±1.658.

解释：

A is correct. The two samples are drawn from two different time periods, so they are independent samples. The population variances can be assumed to be equal. Under all considerations, the t-test has 60+60-2=118 degrees of freedom.For a two-tailed test, at the significant level of 0.05, the rejection points are ±1.980, so we will reject the null if t<-1.980 or t>1.980.

老师你好，我想问以下几个问题：


  1. 这道题是不是因为总体方差未知，所以要用t分布查表？
  2. 这里的significant level是0.05， 我可以看成是5%吗？ 然后是因为双尾，所以中间的interval是95%， 所以critical value是±1.96。
  3. 因为我没有原版书，请问在网站哪里可以找到T分布的图表？


谢谢老师！

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1 个答案
已采纳答案

星星_品职助教 · 2020年06月03日

同学你好，

1. 这道题通过原假设就可以看出这是一个关于mean difference的检验，对应的检验方法直接就是t检验，没必要专门去考虑总体方差的问题了

2. significant level用小数还是百分数表示没有区别，都是5%的意思。

要注意这道题是假设检验的考点，不再是置信区间的了。所以是单尾还是双尾检验需要看的是备择假设，本题备择假设为Ha: μ1 – μ2 ≠ 0，所以是双尾检验的情况。

可以简单的这么想，不等于0（不在0附近）有两种情况，分布左侧远小于0（左尾），和分布右侧远大于0（右尾），所以拒绝域是左尾和右尾两个。

3. t分布表上传到了学员资料下载处，如果找不到可以咨询辅导员。

 

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