Is the die fair? You suspect that a die has been altered so that the outcomes of

Question

Is the die fair? You suspect that a die has been altered so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You toss the die 600 times and obtain the following results:

Outcome 1 2 3 4 5 6

Count 89 82 123 115 100 91

a) Compute the expected counts that you would need to use in a goodness-of-fit test for these data.

b) Perform the significance test. Refer to the previous exercise. Find the chi-square test statistic and its P-value and write a short summary of your conclusions.

Explanation / Answer

a) H0: The die is fair

H1: The die is not fair

The expected counts are calculated as follows

b)  Test Statistic, X^2: 12.8000

Num Categories: 6
Degrees of freedom: 5
Critical X^2: 11.07051

P-Value: 0.0253

Here Chisquare value > Chisquare critical value and P-value < alpha 0.05, so we reject H0

thus we conclude that the die is not fair

Die Observed Expected Output Freq (Oi) Probability Freq Ei (Oi-Ei)^2 /Ei 1 89 0.167 100 1.21 2 82 0.167 100 3.24 3 123 0.167 100 5.29 4 115 0.167 100 2.25 5 100 0.167 100 0 6 91 0.167 100 0.81 Total: 600 600 12.8

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