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

applying chi sqiare goodness of fit on above:

for above degree of freedom =11-1 =10 as well chi stat X2 =12.8014

p value =0.2350

as P value is not significantly low we can not reject that die is fair.

Please reply

observed Expected Chi square Digit Probability O E=total*p =(O-E)^2/E 2 1/36 7.00 11.92 2.03 3 1/18 30.00 23.83 1.60 4 1/12 32.00 35.75 0.39 5 1/9 35.00 47.67 3.37 6 5/36 65.00 59.58 0.49 7 1/6 71.00 71.50 0.00 8 5/36 57.00 59.58 0.11 9 1/9 55.00 47.67 1.13 10 1/12 45.00 35.75 2.39 11 1/18 24.00 23.83 0.00 12 1/36 8.00 11.92 1.29 429 429 12.8014

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