A die is said to be fair if the probability of rolling the n

A die is said to be fair if the probability of rolling the number i is pi = 1/6 for i = 1, ....,6. You roll a die 480 times with the following outcome. (a) Calculate the test statistic X^2 for the test H0 : the die is fair, versus H4: the die is not fair. using the formula (b) Use the R function pchisq() and the value of the test statistic from (a) to find the p-value for the test in (a). p-value = [ ]

Solution

H0: p = 1/6

Ha: All probabilities are not equal

Two tailed chi square test

Let us prepare contingency table as follows:

i	1	2	3	4	5	6
O	103	63	80	73	88	73	480
E	80	80	80	80	80	80	480
Chi square	0.031518217
Deg freedom	5
p value	0.9999