On the first day of this class we talked about rolling two dice and kept track o

Question

On the first day of this class we talked about rolling two dice and kept track of the sums. Here is a summary of the data from one class. Calculate the average sum that was rolled by the class. So, as a group they rolled 7 2's, 30 3's, etc. We now know that the sum of two dice should have a distribution with a mean of 7, and a standard deviation of sigma = 2.45. Assume that the dice used by our class all came from the same group of dice manufactured in Lot #451 by the Acme Dice Company. Does the mean roll by our class give evidence that Lot #451 produced dice that are NOT fair, or that the dice produce results that are DIFFERENT than a group of fair dice.

Explanation / Answer

as for a fair pair of dice P(X=2)=P(X=12)=1/36

P(X=3)=P(X=11)=2/36=1/18

P(X=4)=P(X=10)=3/36=1/12

P(X=5)=P(X=9)=4/36=1/9

P(X=6)=P(X=8)=5/36

P(X=7)=6/36=1/6

hence from chi square goodness of fit:

for 10 degree of freedom and at 0.05 level; critical value =18.307

as test stat 12.6636 is lower then critical value we can conclude that die is fair.

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E 2 1/36 7.000 11.89 2.01 3 1/18 30.000 23.78 1.63 4 1/12 32.000 35.67 0.38 5 1/9 35.000 47.56 3.31 6 5/36 64.000 59.44 0.35 7 1/6 71.000 71.33 0.00 8 5/36 57.000 59.44 0.10 9 1/9 55.000 47.56 1.17 10 1/12 45.000 35.67 2.44 11 1/18 24.000 23.78 0.00 12 1/36 8.000 11.89 1.27 1 428 428 12.6636

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