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刘恒君 · 2022年03月21日

T分布

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.

为什么是T分布不是Z分布呢 从题干哪里可以判断哇


1 个答案

星星_品职助教 · 2022年03月21日

同学你好,

z分布的适用范围很窄,只有在检验均值是否等于一个固定的数字时才会用到,而且还需要有总体方差已知的前提或者是N很大。

本题检验两个均值是否相等,对应的是t分布。

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