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TheaYu · 2020年04月23日

问一道题：NO.PZ2018062016000140 [ CFA I ]

  1. CFA I
  2. Quantitative

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.

这里n大于30了，为什么不可以用z分布，而是t分布？
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3 个答案

星星_品职助教 · 2020年05月31日

@miumiu

同学你好，这个问题和上一个回复的问题本质是同一个。

1.96对应的是“正态分布”下的关键值。而本题是t分布，所以关键值和正态分布比会略有差异，且是会略大于正态分布的关键值。

miumiu · 2020年05月31日

95%对应的不是1.96吗？

星星_品职助教 · 2020年04月23日

同学你好，

用什么分布并不是由n决定的，而是由所需要检验的情况决定的。类似这道题需要用的就是t检验。

当N很大的时候，t会趋近于正态，所以如果受限制没法直接用t的时候只能退而取其次用z做一个替代。但这是不得已的选择，首选还是用t最精确。

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