Spooky statistics: Halloween puzzle
Test your statistical intuition
In applied statistics, we often use the mean as a summary statistic. We learn about the law of large numbers and the central limit theorem in our introductory statistics classes, and hence use the sample mean as an estimate of the population mean and assume its sampling distribution is (roughly) normal. We also use the sample standard error s/√N to quantify our uncertainty in our estimate of the true mean.
I have written a program that generates independent (pseudo) random samples (click on the link to see a random sample). Pretend like this is an unknown population about which you are trying to learn. I have three questions, to which I’ll reveal the answers after Halloween:
- Give an estimate of the expected value of the population from which these samples are drawn.
- Along with the estimate above, provide a standard error (or similar statistic) for the estimate.
- What is the sampling distribution of the sample mean x̅ for N = 10, N = 100, and N = 1,000?
If you’d like to make it easier to read the samples into your favorite analysis program, you might use something like this function for R. Don’t give away the answer, but I would like to see how you approach the problem (you might, for instance, use Rpubs if you use RStudio). If you have had a mathematical statistics course, this puzzle is probably not for you (you’ll not be surprised) but don’t ruin it for those who might be surprised!
