##### Question

In: Statistics and Probability

# A die is rolled 60 times with the following results for the outcomes 1, 2, 3,...

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

## Solutions

##### Expert Solution

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

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