difficult statistics question................................. see below

Question

4. (Hypothetical) You are conducting research on the prevalence of severe binge drinking among college students. You define severe binge drinking as consuming 10 or more alcoholic beverages at a single sitting. You ask the question: “On how many days in the past two weeks have you consumed ten or more drinks at one time? The answers can range from 0 to 14. You collect data on a sample of 900 students. The average for this sample in 1.37 with a standard deviation of .80. Construct a 95% confidence interval for the average binge drinking score in the population. Another student who reviewed your figures, says your math is correct, but using the normal distribution isn’t correct because the binge drinking scores are highly skewed, with some students binging very frequently, and the majority of students never binge drinking at all. Is she correct that it is inappropriate to calculate a confidence interval for this research question?

Answer 1

Hannah,

            It's important to distinguish between the distribution of binge drinkers in the world and the distribution of sample means of size 900. From Wikipedia

 

the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution.

 

I think in your situation you are justified in using the Normal distribution to calculate the confidence interval for the mean.

 

Hope this helps.

 

Jim

Answer 2

Hannah:

 

The answer is no, she is not correct.  Even though the distribution is highly skewed, a sampling distribution where n=900 will be normally distributed - Central Limit Theorem.

 

Hope this helps,

 

- Rob