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曾兰芝🍒 · 2021年02月17日

老师，为什么题干这种检验师t分布，5年师60个月，n足够大，不是可以认为是z分布吗。。。。

  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.

老师，为什么题干这种检验师t分布，5年师60个月，n足够大，不是可以认为是z分布吗。。。。

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2 个答案

星星_品职助教 · 2021年02月17日

@曾兰芝🍒 回复追问：

这张表的前两行是假设检验里重点学习过的“均值是否等于一个特定的数”的检验，不会在这里来考。

从第三行开始，按照考纲的要求是可以“识别”出哪种情况下对应哪一个检验。并不是很重要的考点。

如果还没学到，那么基础班对应部分掌握一下就可以，此外做到涉及到这张表的题目时，可以记忆一下结论。

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我的答题系统和学员的不一样，看不到题目和知识点的对应关系。这个表是在数量的最后部分讲到的，讲义上也是在很后面。

曾兰芝🍒 · 2021年02月17日

我看到T表下面有写使用方法了。谢谢

星星_品职助教 · 2021年02月17日

同学你好，

关于“n足够大，不是可以认为是z分布”，这个只是近似于z分布。事实上绝大多数分布的n大到一定程度后都近似z分布。但不能说只用一个z分布就可以分析所有的情况了。

如果当我们知道某种情况下有具体对应的分布时，还是需要用对应的分布，这样更加精确。

例如本题，对应的就是t分布。这种对应关系能够识别出来就可以。

附对应讲义供参考

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