Group Project: Divide the class into two groups of approximately equal size. The students in group 1 will each toss a coin 10 times (n1) and count the number of heads obtained. The students in group 2 will each toss a coin 40 times (n2) and again count the number of heads. The students in each group should individually compute the proportion of heads observed, which is an estimate of p, the probability of observing a head. Thus, there will be a set of values of p1 (from group 1) and a set of values p2 (from group 2). All of the values of p1 and p2 are estimates of 0.5, which is the true value of the probability of observing a head for a fair coin.

(a) Which set of values is consistently closer to 0.5, the values of p1 or p2? Consider the proof of Theorem 5.1 on page 147 with regard to the estimates of the parameter p = 0.5. The values of p1 were obtained with n = n1 = 10, and the values of p2 were obtained with n = n2 = 40. Using the notation of the proof, the estimates are given by

. Then explain further why the values of p2 from group 2 are more consistently closer to the true value, p = 0.5, than the values of p1 from group 1.

You will continue to learn more and more about parameter estimation beginning in Chapter 9. At that point emphasis will put on the importance of the mean and variance of an estimator of a parameter.