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.

Question #1:

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. Show all work.

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

critical value a 0.005 is 18.54

TS = 2.999

since TS < critical value

we fail to reject the null hypothesis

In p-value approacf

p-value = P(X^2 > 2.9994) =CHISQ.DIST.RT(2.999483,6) = 0.808912 > 0.005

hence we fail to reject the null hypothesis

p Oi Ei (Oi-Ei)^2/Ei 0.4425 1309 1325.73 0.211123607 0.0475 140 142.31 0.037496311 0.0211 59 63.2156 0.281121802 0.0039 13 11.6844 0.148129417 0.002 5 5.992 0.16422964 0.0014 7 4.1944 1.876642991 0.4816 1463 1442.8736 0.280739752 1 2996 2996 2.999483519 critical 18.5475842

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