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Olivia.W🌸 · 2024年02月01日

这题啥意思。。。。

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.

这题啥意思。。。。

1 个答案

品职助教_七七 · 2024年02月03日

嗨,从没放弃的小努力你好:


题目说从一个正偏的总体中抽样,抽样的样本容量n很大,问样本的均值服从什么分布。

本题考察中心极限定理:如果n很大,则无论总体是什么分布,样本的均值都近似服从正态分布(C选项正确),此正态分布的均值就是总体的均值(B选项错误),此分布的方差为总体方差除以n(A选项错误)。

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