Question

7. Is the die fair? You suspect that a die has been changed so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You to the die 600 times and obtain the following result. Outcome Count 1 2 3 4 87 80 125 117 5 6 10091 - 1 - 1

Answer 1

Answer:

Given that:

Outcome	1	2	3	4	5	6
Count	87	80	125	117	100	91

lets enter the data in excel and then perform a chi sqaure distribution test , which compares the actual distribution of the event with the expected distribution .

If the p value of the test is less than 0.05(assumed alpha) we can conclude that the dice is biased , else we cannot conclude that the dice is not biased

$H_0$ : The dice is not biased

$H_1$  : The dice is biased

Expected count Outcome Count 1 87 100 2 80 100 125 100 4 117 100 5 100 100 6 91 100 Chi square test 0.007950704

Outcome Count Expected count 600*1/6 1 87 600*1/6 2 80 -600*1/6 125 600*1/6 4 117 600*1/6 600*1/6 5 100 6 91 =CHISQ.TEST(B2:B7,C2:C7) Chi square test

now the chisq.test function gives the p value of the result , which in this case is 0.0079 and is less than 0.05 hence we can reject the null hypothesis in favor of alternate hypothesis and conclude that The dice is biased .

The expected frequency for each outcome is 600*1/6 , as we would expected each dice to have an equal chance of appearing .