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
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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