Sampling Distribution when Population Not Normal, but Standard Deviation Known

When the underlying population is not normally distributed, but its standard deviation is known, we cannot assume the sampling distribution of the mean is normally distributed for small sample sizes, right?

I'm having trouble finding information for this scenario.

Thanks.

MathMathter said:

When the underlying population is not normally distributed, but its standard deviation is known, we cannot assume the sampling distribution of the mean is normally distributed for small sample sizes, right?

I'm having trouble finding information for this scenario.

Thanks.

Click to expand...

No. Without going into much detail, the Central Limit Theorem say that irregardless* of the underlying distribution, if you take a lot of groups of sufficient size of samples of the underlying distribution that the means of the groups will be normally distributed with a mean of the underlying distribution. The 'sufficient size' of the group will vary depending on the underlying distribution but somewhere around 30-50 should be good for 'any distribution'. The following gives some examples for different sizes of the group for the uniform distribution
http://www.statisticalengineering.com/central_limit_theorem.htm


http://stattrek.com/sampling/sampling-distribution.aspx
talks about sufficient sample sizes



*yes, i know, but I like the work and it is in the dictionary.

Thanks for verifying that. The illustrations in your first link are especially helpful!