You have an ordinary six-sided die, but you suspect it may be loaded. If the die is fair, then the probability of rolling a 6 equals 1/6.

a. Let π = the probability of rolling a 6. To estimate π to within 0.01 at the 95% confidence level, you need a sample size of ____________.

b. The SD for p̂ is √{π(1 − π)/n}. What values of π give a value of 0 for the SE? Explain why this result makes sense.

c. Compute the value of π(1 − π) for values of π = 0, 1/4, 1/2, 3/4, 1. Plot the points with values of π on the x-axis and join the points with a smooth curve. What value of π gives the larges possible value for SD(p̂)?