Midterm Exam, Page 6 of 9
1 May 2014
4. Imagine that you work for the Nevada Gaming Commission, checking that games of chance played in casinos actually
have the advertised chances of winning and losing. You are tasked with evaluating a game which has two outcomes–
winning $1.50 or losing $1. The usual procedure for evaluating games is to perform a hypothesis test, where the null
hypothesis is that the game’s outcomes occur with the chances that the casino claims, and the alternative hypothesis
is that the game’s outcomes do not occur with the chances that the casino claims.
If the p-value is statistically
significant, the game is considered discredited, and must be closed. If it is not statistically significant, the game may
remain open. When you arrive at the casino to test the game, you have forgotten the paperwork which tells you what
the chances for the two outcomes should be, so you are unable to perform a test.
(a) (3 points) Your assistant suggests that since you cannot complete a hypothesis test, you can instead calculate a
confidence interval for the chance of winning. What do you think of this plan? Explain. If you agree with this
plan, be sure to specify what confidence level the interval should have and why.