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 90 times and come up with the following distribution:

1	2	3	4	5	6
15	14	20	12	15	14

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

a) One proportion z test; z = 2.110

b) χ² Goodness of Fit; χ² = 4.074

c) χ² Goodness of Fit; χ² = 2.400

d) Two proportion z test; z = 0.082

e) One proportion z test; z = 0.082

f) None of the above

Answer 1

using minitab

enter dataa>stat>tables>chi square goodness of fit>select coloumn>select equal proportions>ok

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: C1

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 15 0.166667 15 0.00000
2 14 0.166667 15 0.06667
3 20 0.166667 15 1.66667
4 12 0.166667 15 0.60000
5 15 0.166667 15 0.00000
6 14 0.166667 15 0.06667

N DF Chi-Sq P-Value
90 5 2.4 0.791

answer is χ2 Goodness of Fit; χ2 = 2.400