DS 10.3.1 gives the results of n = 500 die rolls.
(a) What are the expected cell frequencies if the die is a fair one?
(b) Calculate the Pearson chi-square statistic X2 for testing whether the die is fair.
(c) Calculate the likelihood ratio chi-square statistic G2 for testing whether the die is fair.
(d) What p-values do these chi-square statistics give? Does a size α = 0.01 test of the null hypothesis that the die is fair reject or accept the null hypothesis?
(e) Calculate a 90% two-sided confidence interval for the probability of obtaining a 6.