Problem 5: Are small samples better? [10 points]

Randomized experiments in marketing are (in)famous for finding very large effects in relatively small samples. Marketers often defend their use of small sample sizes in their experiments with logic like the following: "If my sample size were really large, anything would be statistically significant! Therefore, it's better to use smaller sample sizes since we'll only get significant results when our treatment has a really big impact." Do you agree with this logic? Why?