Chapter 1.2, Problem 16PB

Samples vary less with more data We’ll see that the amount by which statistics vary from sample to sample always depends on the sample size. This important fact can be illustrated by thinking about what would happen in repeated flips of a fair coin.

1. a. Which case would you find more surprising—flipping the coin five times and observing all heads or flipping the coin 500 times and observing all heads?
2. b. Imagine flipping the coin 500 times, recording the proportion of heads observed, and repeating this experiment many times to get an idea of how much the proportion tends to vary from one sequence to another. Different sequences of 500 flips tend to result in proportions of heads observed which are less variable than the proportion of heads observed in sequences of only five flips each. Using part a, explain why you would expect this to be true.