Poker is back. It is so popular that the internet is loaded with on-line poker s
ID: 3355528 • Letter: P
Question
Poker is back. It is so popular that the internet is loaded with on-line poker sites. Johnny C. is a poker enthusiast who believes that a certain on-line site is manipulating the probabilities to encourage winning. He has recorded the results of 3 months of playing with the accepted probabilities for each hand, n = 2,996.
Hand
1 pair
2 pair
3 of a kind
Straight
Flush
Full House
Other
Probability
0.4425
0.0475
0.0211
0.0039
0.0020
0.0014
0.4816
Number of Hands
1,309
140
59
13
5
7
1,463
Expected Values
Test Johnny C’s claim that the on-line games do not follow the accepted probabilities with = .005. Please use the p-value approach, show all work with explanations.
Hand
1 pair
2 pair
3 of a kind
Straight
Flush
Full House
Other
Probability
0.4425
0.0475
0.0211
0.0039
0.0020
0.0014
0.4816
Number of Hands
1,309
140
59
13
5
7
1,463
Expected Values
Explanation / Answer
here null hypothesis: Ho: on-line games follow the accepted probabilities
alternate hypothesis:Ha: on-line games do not follow the accepted probabilities
for degree of freedom =categories-1=7-1=6
applying chi square goodness of fit test:
for above test statistic 2.999 and 6 degree f freedom ; p value =0.8089
as p value is greater than 0.005 level we can not reject null hypothesis
therefore we can not conclude that on-line games do not follow the accepted probabilities
observed Expected residual Chi square x Probability(p) Oi Ei=total*p Ri=(Oi-Ei)/Ei R2i=(Oi-Ei)2/Ei 1 pair 0.4425 1309.000 1325.7 -0.46 0.21 2 pair 0.0475 140.000 142.3 -0.19 0.04 3 of a kind 0.0211 59.000 63.2 -0.53 0.28 straight 0.0039 13.000 11.7 0.38 0.15 flush 0.0020 5.000 6.0 -0.41 0.16 full house 0.0014 7.000 4.2 1.37 1.88 other 0.4816 1463.000 1442.9 0.53 0.28 total 1 2996 2996 0.696047545 2.999