Use the Central Limit Theorem to explain the difference between the sampling distribution of x and...

Use the Central Limit Theorem to explain the difference between the sampling distribution of x and x-bar.

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Expert Solution

Central Limit Theorem states that regardless of the distribution of a population, the distribution of its sample mean is approximately normal if the sample size is large.

So no matter what the distribution of X (population), if we draw large samples from the population, and find the mean of each sample (X-bar), we get a distribution of these x-bars. This distribution of x-bars is approximately normal provided the sample size of each sample drawn from the population was large.

Ex- If we have a population which has a poisson distribution. We collect a large sample from it and find its mean. Then we collect another large sample from the population and find its mean too. Similarly, we repeat this procedure many time finding a mean each time. We will obtain a distribution of means from the poisson distributed population. This resulting distribution would be approximately normally distributed.

So the distribution of X is poisson (for example) but that of X-bar is approximately normal (provided the samples drawn to find x-bars are large).

orchestra answered 1 year ago

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