18. Testing Whether Random Sample is From a Discrete Uniform Population Distribution. Let Xi, i 1,...,n be random sample from some discrete integer-valued population

18. Testing Whether Random Sample is From a Discrete Uniform Population Distribution. Let Xi, i ¼ 1,...,n be random sample from some discrete integer-valued population distribution. Let the range of the random variables be 1,2,...,m.

(a) Describe how you would use the w2 goodness of fit size a test to assess the hypothesis that the population distribution was a discrete uniform distribution with support 1,2,...,m.

(b) The Nevada Gaming Commission has been called in to investigate whether the infamous Dewey, Cheatum, & Howe Casino is using fair dice in its crap games. One of the alleged crooked dice is tossed 240 times, and the following outcomes were recorded:

X Frequency 1 33 2 44 3 47 4 39 5 31 6 46 Does this die appear to be fair? What size test will you use? Why?