Question

USE THE 4 STEP PROCESS

1. We know that the probability of a player winning a dice game at a casino is 49.3%. You observe that in the last 390 games played the player won 198 times.

a) At the .01 level is the player winning at a percentage higher than expected? (note p-value = .281)

b) Does the casino have evidence to conclude the player is cheating based on the test based on a)? explain

c) The 99% confidence interval from the computer says “99%for p is .4488 or more” explain what this means in context of the problem

d) Interpret the p-value

e) What is the only type of error that could have occurred and explain in context

Answer 1

Ans:

a)

sample proportion=198/390=0.5077

Test statistic:

z=(0.5077-0.493)/sqrt(0.493*(1-0.493)/390)

z=0.581

p-value=P(z>0.581)=0.281

As,p-value>0.01,we fail to reject the null hypothesis.

There is not sufficient evidnece to conclude that player is winning at higher percentage than expected.

b)No,casino does not have sufficient evidence that player is cheating.

c)

99% lower confidence bound=0.5077-2.326*SQRT(0.5077*(1-0.5077)/390)=0.4488

As,lower confidence bound is 0.4488,so we are 99% confident that true proportion of winning is 0.4488 or more.

d)If true winninng percentage is 49.3%,then probability of observing 198 or more number of wins out of 390 times is 0.281

e)As,we fail to reject H0,we could make type II error.As,we are concluding that percentage of winning is not more than 49.3%,but in actual ,it may be more than 49.3%.