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Lynn · 2020年07月03日

问一道题：NO.PZ2018062016000140 [ CFA I ]

  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.

为什么degree of freedom 是120-2而不是120-1呢？
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1 个答案

星星_品职助教 · 2020年07月03日

同学你好，

不同t检验的自由度是不一样的，当检验μ是否等于一个确定数的时候，t检验的自由度是n-1。

而这道题检验的是两组数据的均值比较。此时t检验对应的自由度就是n1+n2-2，可以理解为第一组数据的df=60-1=59，第二组数据的df=60-1=59，所以加起来总的df=118

这个检验不是特别的重要，定性的了解即可

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