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欢欢 · 2021年08月18日

双尾95%的概率对应的rejection point不是正负1.96吗？按照老师之前让记住的那四个常用组合

  1. CFA I
  2. Quantitative

NO.PZ2018062016000140

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.

双尾95%的概率对应的rejection point不是正负1.96吗？按照老师之前让记住的那四个常用组合

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星星_品职助教 · 2021年08月19日

同学你好，

±1.96是正态分布下置信区间或双尾检验的关键值。而本题是t分布。

所以需要根据df=118和“significant level is 0.05”去查t分布表。

t分布表可以从学员资料下载处进行下载，也可以直接看原版书附录里的t表。如果对于如何查表有问题也可以继续追问。

欢欢 · 2021年08月20日

自由度118，是因为两个样本各含60个观察值，所以是60➕60➖2对吗？

星星_品职助教 · 2022年06月14日

@18816562889

可以这样理解。

星星_品职助教 · 2022年02月09日

@王秋宇

同学你好，

1）总体是这段时间所有的return。题干表格是按月分割，每段时期都抽出了60个月的月度return，即表格中的数据都是这两个60个样本的样本统计量。

2）其实不用判断，类似的题目一定是用t分布来解的，没有用z分布来解的情况。

王秋宇 · 2022年02月09日

看了您的解释，但是这题目为什么是T分布呢？总体的1-5，6-10都给了，不应该是Zj分布吗？

星星_品职助教 · 2021年08月20日

@欢欢

对的。这种特殊检验的自由度需要格外记忆一下。

18816562889 · 2022年06月14日

老师 请问这个自由度可不可以理解为第一个样本自由度-1，第二个样本自由度也要-1，合在一起就要-2？

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