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许诺 · 2020年09月15日

问一道题: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.

老师,请问关于B选项,两个总体的方差算出来分别为20.052和17.131,是不相等的,为什么作出方差相等的假设呢?

1 个答案

星星_品职助教 · 2020年09月15日

同学你好,

这道题目总体的方差是不知道的,题干给出的所有信息都是样本的。所以才用t检验,t检验的前提是总体方差未知。

如果这道题的两个总体方差已经确切的知道了,就没有去做假设检验的必要了

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