Let review an example to check if die is balanced. Under the null hyphotesis, we

Question

Let review an example to check if die is balanced.

Under the null hyphotesis, we would assume that the probabilityof a specific side coming up when we roll this die is 1/6. To test this notation, we can roll the given die a specific number of times and observe the frequency for each outcome.

Suppose we roll this die 180 times and obtain the frequencies for various outcomes as listed in the following table.

The larger question is how do you test to see if a die is a fair die? Do the differences listed from the 180 rolls of one supposedly fair die cause concern for you?

Outcome 1-spot 2-spot 3-spot 4-spot 5-spot 6-spot Frequency 26 31 29 33 26 35

Explanation / Answer

here applying chi square goodness of fit on above . as probabilty of a digit on a die =1/6 =0.1667

hence

for above chi stat =2.267

and degree of freedom =5

from chi sqaure table ; p value =0.8111

as p value is very high, we can not conlude that die is unfair or baised,

observed Expected Chi square P O E=total*p =(O-E)^2/E 1 0.167 26.00 30.00 0.53 2 0.167 31.00 30.00 0.03 3 0.167 29.00 30.00 0.03 4 0.167 33.00 30.00 0.30 5 0.167 26.00 30.00 0.53 6 0.167 35.00 30.00 0.83 180 180 2.267

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