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chuziyang · 2022年05月08日

|t-statistic|為多少

  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.

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


請問|t-statistic|為多少？這題如何計算，謝謝，

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1 个答案

星星_品职助教 · 2022年05月08日

同学你好，

这道题不需要计算t-statistic。independent sample背景下的检验有个复杂的公式，考计算的概率不大。

本题需要判断的是critical value。能知道此时的自由度是n1+n2-2，查表得到关键值就可以选出A并排除B、C了。


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