Directions: Please use the P-value Approach for all hypothesis tests. Follow all

Question

Directions: Please use the P-value Approach for all hypothesis tests. Follow all the steps used in hypothesis testing as delineated in the guided notes or the textbook and be sure to verify the conditions for each test. Include any StatCrunch, SurfStat, graphing calculator, etc... output used in the process. I am assuming that all questions will be answered using technology-it is not necessary to include by-hand construction of the test statistics. Assume that all samples are randomly obtained. 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. a) Test Johnny C's claim that the on-line games do not follow the accepted probabilities with alpha = 005. b) There are many other poker hands that were lumped into the "Other" category (IE: Royal Flush, probability of 0.000015391). Why did Johnny C. have to place these hands into one category?

Explanation / Answer

Ans:

H0:On line games follow the accepted probabilities.

H1:On line games do not follow the accepted probabilities.

Calculated chi square score=2.999

number of categories=7

degrees of freedom=7-1=6

significance level=0.005

Critical chi square score=CHIINV(0.005,6)=18.55

As,calculated chi square score=2.999<18.55,we fail to reject null hypothesis.

we have sufficient evidence to reject the claim that on line games do not follow the accepted probabilities.

1 pair 2 pair 3 of a kind straight flush full house other Total Probability 0.4425 0.0475 0.0211 0.0039 0.002 0.0014 0.4816 1 Number of hands(O) 1309 140 59 13 5 7 1463 2996 Expected(E) 1325.73 142.31 63.22 11.68 5.99 4.19 1442.87 2996 (O-E)^2/E 0.211 0.037 0.281 0.148 0.164 1.877 0.281 2.999

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