Question

Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical probabilities for each roll should be:

1	2	3	4	5	6
16 2/3 %	16 2/3 %	16 2/3 %	16 2/3 %	16 2/3 %	16 2/3 %

You roll the die 93 times and come up with the following distribution:

1	2	3	4	5	6
15	13	21	14	15	15

What type of test should be used in this situation and what is the test statistic?

a) χ² Goodness of Fit; χ² = 2.548

b) One proportion z test; z = 0.161

c) One proportion z test; z = 1.230

d) χ² Goodness of Fit; χ² = 4.074

e) Two proportion z test; z = 0.161

f) None of the above

Answer 1

If a die is rolled each side is equally probable. Probabilty of each side 16.67 % or 1/6 .

Expected count for each side is = 93 * (1/6) = 15.5.

Number on face	Observe count	Expected count
1	15	15.5
2	13	15.5
3	21	15.5
4	14	15.5
5	15	15.5
6	15	15.5

I shall use 2 goodness of fit.

2 = ( observed - expected ) ^2 / expected = (15- 15.5 )^2 / 15.5 + ... + (15- 15.5 )^2 / 15.5 = 2.548

So, option a) is correct.

Feel free to comment if you need any clarification.

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