Ordinary dice have six equally likely sides. You can buy dice online with (A) 4 sides, (B) 6 sides, (C) 8 sides, or (D) 10 sides. Suppose you want to estimate the probability of rolling a 1 for each of dice (A)–(D).
a. Which die (A)–(D) will give an estimate for the probability of rolling a 1 with the largest SD?
b. Explain your answer in part (a).
c. Suppose the 10-sided die is in fact fair. If you roll 25 times and estimate the probability of rolling a 1, your SD for pˆ will be ______.
d. Continue to suppose that the 10-sided die is fair. You want your estimate of π to have an SE of 0.01. How large should your sample size be?