This time you are researching alcohol addiction among convicted felons. You used

Question

This time you are researching alcohol addiction among convicted felons. You used an “Alcohol Addiction” Scale where a score of 1 indicates no addiction to alcohol and higher scores, up to a maximum of 10, indicate increasing addiction to alcohol. With the help of a team of researchers, you’ve gathered data from 3000 samples, all of size n=100. You found that the means of these samples yielded a normal distribution. From this, what do you know about the distribution of your variable, alcohol addiction, in the population of convicted felons? Why?

Explanation / Answer

The distribution of the population can be anything.

Why?
Because in this case n = 100. Which is greater then 30. Hence the distribution of the sample means follow Celtral Limit Theorem.

The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.

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