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When you have the parental population that is highly skewed, you can make the sample size...

When you have the parental population that is highly skewed, you can make the sample size larger than 30 to make an accurate Xbar chart. In this case, what is the relationship between the sample size and standard deviation (dispersion)?Justify your answer based on the Central Limit Theorem
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Answer #1

According to the central limit theorem, as the sample size is increased more and more and specifically when it is greater than 30, we can approximate the sampling distribution of the sample means as a normal distribution such that:

Where n is the sample size.

Therefore the relationship between standard deviation of the sampling distribution of sample means and the sample size is given as:

Which shows that the standard deviation of the sample means is inversely proportional to the square root of the sample size n.

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