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zoewong · 2022年04月04日

怎麼算出來的1.98

  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.

可以詳細講一下做題思路嗎


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星星_品职助教 · 2022年04月04日

同学你好，

1.98为critical value，为查表得到。

对于检验两组mean是否相同，且独立样本的情况。应使用t检验，自由度为n1+n2-2。得到本题的自由度为60+60-2=118 （B选项错误）

根据significance level=0.05和双尾检验，可知单尾面积为0.025。再结合自由度=118（取最接近的120），即可查表得到critical value≈1.98 （C选项错误）

由于拒绝原假设的原则为|t-statistic|＞|critical value|，可知A选项正确。


forri · 2022年06月22日

考试会考这种查表的题目？

Pavel Korchagin · 2023年01月17日

n1+n2-2这个自由度在哪一章

星星_品职助教 · 2023年01月18日

@libaicun

M6的如下内容：

星星_品职助教 · 2022年06月23日

@forri

会，查表需要掌握

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