To locate treatment programs for heroin addicts the mayor wa

To locate treatment programs for heroin addicts, the mayor wants to conduct a study of persons arrested for possession in your city.

He suggests looking at data on location of arrest and residence of arrestees for the past month. This will yield a sample of at least eighty cases. From his statistics course, he says that with a sample size greater than 50, the central limit theorem will apply and you can to make a reasonable estimate of the numbers of people needing treatment with a level of confidence of 95%.

Is the mayor correct? Would you suggest a different sampling plan? If yes, what would you suggest?

Solution

Yes, the mayor is correct. As the sample size (=50) is large, Central Limit Theorem can be applied. Criminal justice is independent of location of arrest and residence of arrestees, hence it can lead to biasness, and thus random sampling would be more appropriate.