| Summary: | This report evaluates whether normal approximation or resampling is to prefer for estimating the distribution of the sample mean and functions of the sample mean. The evaluation relies on simulation studies. The observations of the sample are allowed to be differently distributed. In the case of sample means they are also allowed to be dependent. For sample means the two approximations behaves very similar. The most important component whether we have a good or a bad approximation is how good the approximations catch the variance of the true distribution. In this case the normal approximation is to prefer, because it’s easier to use. For functions of sample means, it is possible that the distribution is very skewed. In this case resampling performs better than the normal approximation. This is mainly due to the fact that resampling, but not the normal approximation, can catch the skewness of the true distribution.
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