Question

Playing Dice 1 point possible (graded) You and your friend play dice games for fun, but one day you suspect that the die your friend uses is not fair. You will gather data and use the tools of hypothesis testing in this problem to provide a plausible answer as to whether or not the die is tan Pp Your statistical model is ({1,2,3,4,5,6},{Pp ). You roll the die 15 times, writing the sample as random variables X1,..., X15 where p is the true parameter. Your null and alternative hypothesis are, respectively. H:p p - [1/6 1/6 1/6 1/6 1/6 1/6). [1/6 1/6 1/6 1/6 1/6 1/6)". H Let p denote the MLE for the true parameter p. You use the following test statistic to test the hypotheses: To - nag , -1) T., converges to a random variable X X for some integer k. What is k?

Answer 1

Here Tn is nothing but the chisquare goodness of fit test statistic. So k=number of categories -1

Here, number of categories is 6.

Hence k=6-1=5