Roll two dice and record the difference

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Question from Barbara:

Suppose you roll two dice 100 times. Each time you record their difference (always subtracting the smaller one from the bigger one to get a positive difference). The possible values you get are 0,1,2,3,4 and 5. You record the frequency of each value in the following table:
Difference of two dice 0 1 2 3 4 5
Observed frequency 12 31 26 13 10 8
Let your null hypothesis be that the dice are fair, and the alternative hypothesis be that they are not fair. Using a confidence level of α = 0.10, test the null hypothesis by a goodness-of-fit test.

Hint: begin by
completing table:
x 0 1 2 3 4 5
f(x)

Hi Barbara,

Under the hypothesis that the dice are fair construct a table similar to what I created in my response to Jose but rather than recording the sum of the numbers on the two dice, record the difference. If the dice are fair then the probability of landing in each of the 36 cells is $\large \frac{1}{36}.$ Hence you can calculate the probabilities of obtaining a 0, 1, 2, 3, 4, and 5 and hence the expected number of 0s, 1s, up to 5s in 100 rolls. With these expected numbers and observed frequencies you can construct a goodness-of-fit test.

Write back if you need more assistance,
Penny

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