Im working through a textbook atm and Ive read that the mean of "the sampling distribution of means" is the same as the "populations" mean.

To construct the sampling distribution of means, i need to take X * number of independent samples (where each sample is composed of >= ~30 observations) from the population, calculate the mean of each sample and plot the mean.

Q1: Whats the minimum value that X (the number of means used to construct the sampling distribution) should be, or do you typically plot the distribution and increase X until it begins to look normal?

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There really are 2 concepts here. The exact or theoretical sampling distribution consists of every possible sample from the population. The approximate sampling distribution is the result of a large number of samples.

When we make statements like the mean of the sampling distribution is equal to the mean of the population then we are talking about the exact or theoretical sampling distribution. The mean of the approximate sampling distribution will be close to the population mean, but is unlikely to be exactly the same due to sampling error.

The approximate distribution is usually easier to demonstrate and can be a good approximation to the exact one, so they are often used interchangeably, but for a full understanding you should understand that all the theory is based on the exact which includes every possible sample from the population of size n. For non-small population sizes that number is either infinity or a value close enough to infinity to not make a practical difference, which is why the approximation is often shown/demonstrated.

So the answer is either infinity/all of them, or enough that you are happy with the approximation.

Also, there is nothing magical about the number 30, sampling distributions work for smaller sample sizes. There are some populations that will generate near normal sampling distributions with n=10, while others will still not be close enough to normal at n=100.

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  • $\begingroup$ Thanks very much for clarifying that, i really appreciate it. Ive had some issues with this for a while + the difference between sample and population. $\endgroup$ – Hans Rudel Feb 7 '13 at 22:15

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