Question: A casino player has grown suspicious about a specific roulette wheel. Specifically, this player believes that the slots for the numbers 0 and 00, which can lead to larger payoffs, are slightly smaller than the rest of 36 slots, which means that the ball would land in these two slots less often than it would if all of the slots were of the same size. This player watched 430 spins on this roulette wheel, and found that the ball landed in 0 or 00 slot 14 times.
a. What is the value of the point estimate of the proportion of all roulette spins on this wheel in which the ball would land in 0 or 00 slot?
b. Construct a 95% confidence interval for the proportion of all roulette spins on this wheel in which the ball would land in 0 or 00 slot.
c. If all of the slots on this wheel are of the same size, the ball should land in 0 or 00 slot 5.26% of the time. Based on the confidence interval you calculated in part b, does the player's suspicion seem reasonable?