Question

1. A die is rolled 60 times with the following results for the outcomes 1, 2, 3, 4, 5, and 6, respectively: 13, 7, 6, 11, 10, and 13.
   1. Specify the null and alternative hypotheses.
   2. Use Minitab to perform the analysis. What is the conclusion?
   3. Show how to obtain by hand the found in the Minitab output.
   4. Demonstrate how to find the bounds on the p-value using a table

Answer 1

Null Hypothesis: die is Fair

alternate hypothesis: die is not fair

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Minitab output-

since, p value >α=0.05, fail to reject Ho

conclusion: die is fair

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observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
13	0.17	10.000	3.00	9.00	0.900
7	0.17	10.000	-3.00	9.00	0.900
6	0.1667	10.000	-4.00	16.00	1.600
11	0.1667	10.000	1.00	1.00	0.100
10	0.1667	10.000	0.00	0.00	0.000
13	0.1667	10.000	3.00	9.00	0.900

chi square test statistic,X² = Σ(O-E)²/E =   4.4000              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   6   -   1   =   5
                  
P value =   0.4934   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value >α , Do not reject Ho