In 360 tosses of a pair of dics 74 seven and 24 elevens are oserbved. Using the 0.05 significance level, test the hypothesis that the dics are fair

Answer 1

Pr(7)=6/36 , Pr(11)=2/36. In 360 tosses expected number of 7's=60 and the expected number of 11's=20.

Using the Chi-square goodness of fit test the calculated value is of Chi-square is

{(74-60)^2/60 +(24-20)^2/20}=4.06667. The p-value is 0.0437. Since this is less than 0.05 the dice are not fair.