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v · 2024年04月30日

样本足够大不是也可以用Z检验吗？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000147

问题如下：

An analyst is examining the monthly returns for two funds over one year. Both funds’ returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use:

选项：

A.

a parametric test only.

B.

a nonparametric test only.

C.

both parametric and nonparametric tests.

解释：

B is correct.

There are only 12 (monthly) observations over the one year of the sample and thus the samples are small. Additionally, the funds’ returns are non-normally distributed. Therefore, the samples do not meet the distributional assumptions for a parametric test. The Mann–Whitney U test (a nonparametric test) could be used to test the differences between population means

这道题检验的是两个均值之间的关系。如果对应的两个总体都是正态分布的话，那么我们需要使用t检验，也就是参数检验（对于t检验而言，参数就是自由度df）。

但这道题为非正态总体“Both funds’ returns are non-normally distributed”，所以t检验就不能用了。这个时候只能使用非参数检验。

非正态分布，样本足够大不是也可以用Z检验吗？

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1 个答案

品职助教_七七 · 2024年04月30日

嗨，爱思考的PZer你好：


这道题检验的是两个均值之间的关系。这个检验背景下如果想用参数检验的话，需要使用的是t检验，不能使用z检验。

题干中提示的条件：1）小样本；2）非正态总体都是针对t检验的，在这种情况下t检验无法使用，所以只能考虑非参数检验。整道题和z检验都是没关系的。

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2022-09-28 12:08 1 · 回答

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2022-09-28 11:53 1 · 回答

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