NO.PZ2022123001000088
问题如下：
There are three fat-tailed samples.The followings are their standard error of the sample mean and sample variance. Which sampling distribution of the sample mean has fatter tails?
选项：
Standard error of the sample mean
Sample variance
5
100
2
64
3
81
解释：
With the knowing standard deviation and standard error, the sample size(n) is:
nA=4; nB=16; nC=9
According to the central limit theorem, a sampling distribution of the sample mean will be approximately normal only if the sample size n is large. As n increase, the sampling distribution of the the sample mean will has less fat tails. So A with a smallest size is correct.
这道题的解析不是很明白，n越大越接近正态分布可以理解，但是偏离正态分布也有可能是platylkurtic，那相较于normal distribution就是thin-tailed，为什么这边就默认样本量越小就只是leptokurtic（fat-tailed）的情况，是不是还有其他条件没考虑到？还请老师再解答一下。谢谢
