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娈安 · 2024年09月26日

positively skewed在这个题目里是什么意思

NO.PZ2022123001000087

问题如下:

If the distribution of the population from which samples of size n are drawn is positively skewed and given that the sample size, n, is large, the sampling distribution of the sample means is most likely to have a:

选项:

A.variance equal to that of the entire population.

B.mean smaller than the mean of the entire population.

C.distribution that is approximately normal.

解释:

Given a population that has a finite variance and a large sample size, the central limit theorem establishes that the sampling distribution of sample means will be approximately normal, the distribution of sample mean will have a mean equal to the population mean, and will have a variance equal to the population variance divided by the sample size.

我也知道中心极限定理,但是被positively skewed 误导了

1 个答案

品职助教_七七 · 2024年09月26日

嗨,努力学习的PZer你好:


中心极限定理说明的是无论总体是什么分布,n足够大时样本均值都(近似)服从正态分布。

这里positive skewed就是刻意去说明总体不服从正态,欲以此造成误导。但无论总体是否服从正态分布,都不影响样本均值会去(近似)服从正态分布。

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