Case Problem 3: Fresno Board Games Fresno Board Games manufactures and sells several different board games online and through department stores nationwide. Fresno's most popular game, Cabestrillo Cinco!, is played with 5 sixsided dice. Fresno has purchased dice for this game from Box Cars, Ltd., for twenty-five years, but the company is now considering a move to Big Boss Gaming, Inc. (BBG), a new supplier that has offered to sell dice to Fresno at a substantially lower price. Fresno management is intrigued by the potential savings offered by BBG, but is also concerned about the quality of the dice produced by the new supplier. Fresno has a reputation for high integrity, and its management feels that it is imperative that the dice included with Cabestrillo Cinco! are fair. To alleviate concerns about the quality of the dice it produces, BBG allows Fresno's manager of product quality to randomly sample five dice from its most recent production run. While being observed by several members of the BBG management team, Fresno's manager of product quality rolls each of these five randomly selected dice 500 times and records each outcome. The results for each of these five randomly selected dice are available in the file BBG. Fresno management now wants to use these data to assess whether any of these five six-sided dice is not fair; that is, does one outcome occur more frequently or less frequently than the other outcomes? Managerial Report Prepare a managerial report that addresses the following issues. 1. Use descriptive statistics to summarize the data collected by Fresno's manager of product quality for each of the five randomly selected dice. Based on these descriptive statistics, what are your preliminary conclusions about the fairness of the five selected dice?

Use the data collected by Fresno's manager of product quality to test the hypothesis that the first of the five randomly selected dice is fair, i.e., the distribution of outcomes for the first of the five randomly selected dice is multinomial with p1 = p2 = p3 = p4 = p5 = p6 = 1/6. Repeat this process for each of the other four randomly selected dice. Use a = .01. Do the results of your hypothesis tests provide evidence that BBG is producing unfair dice?

Die
1	2	3	4	5
5	2	5	2	5
4	3	5	1	2
2	4	2	1	2
4	1	3	5	1
1	5	4	2	1
4	6	3	1	6
4	6	3	5	5
2	2	6	2	1
6	5	4	4	1
2	5	2	2	2
3	5	1	2	4
6	3	5	3	5
1	6	1	5	5
6	3	6	2	4
2	4	6	2	3
6	1	2	3	3
3	6	2	1	4
1	1	1	1	4
6	3	5	2	1
2	2	5	4	5
3	6	6	4	4
1	2	1	1	2
1	4	3	2	6
4	4	4	1	6
4	1	1	5	5
5	4	3	5	6
2	4	1	5	1
1	6	5	6	1
6	2	2	6	2
5	1	6	2	4
1	4	6	3	1
5	3	6	3	3
1	6	1	1	4
5	4	1	5	3
2	5	6	3	3
5	4	1	4	3
6	3	6	2	4
4	4	5	3	2
1	1	6	3	6
6	4	5	5	5
1	4	2	5	1
4	1	5	6	1
5	1	6	5	4
1	6	4	5	3
3	1	5	3	3
5	5	3	3	1
6	1	1	6	6
1	4	3	1	2
4	4	1	4	4
5	5	4	2	3
6	4	2	6	2
3	5	1	3	6
5	3	1	5	2
4	6	4	3	2
2	2	3	4	2
2	4	5	2	2
1	2	2	2	5
1	4	5	4	3
6	2	2	6	4
1	2	4	1	6
5	6	2	2	5
3	3	6	4	5
4	2	2	3	5
6	1	2	6	5
2	2	1	6	6
5	3	2	6	5
3	1	5	3	4
4	1	2	4	1
5	2	2	3	3
5	1	6	2	2
4	2	4	1	5
5	6	4	6	2
6	6	6	3	5
3	4	1	4	2
3	5	6	6	6
3	5	2	2	5
4	4	6	1	3
1	5	3	3	5
6	1	6	5	2
6	5	5	6	3
5	2	1	6	5
4	6	4	6	2
4	5	4	1	1
2	5	2	4	1
1	2	6	1	2
5	1	2	2	2
1	1	4	4	1
5	3	2	5	6
1	1	2	4	2
5	6	1	1	6
1	3	1	4	4
6	3	4	5	5
1	3	2	4	6
5	4	6	6	3
6	2	4	6	1
1	2	3	6	5
1	6	5	4	2
2	5	3	5	3
6	1	3	2	3
2	3	5	4	5
2	2	4	3	4
4	5	6	5	4
1	4	5	1	6
3	4	1	3	6
5	3	5	4	5
4	2	3	1	4
1	5	6	5	1
6	6	2	3	6
6	2	4	2	4
2	1	1	1	6
6	5	2	6	6
2	2	5	2	3
6	6	6	5	5
6	4	3	6	2
1	6	6	1	4
3	6	5	6	2
6	3	6	3	5
3	1	1	2	1
3	6	1	2	4
4	2	3	5	3
2	6	1	1	5
1	6	5	6	1
1	4	1	6	1
4	1	5	1	6
3	3	5	2	2
1	4	4	1	2
2	2	2	3	1
2	6	4	1	3
1	6	6	5	4
5	2	3	6	6
4	3	5	1	2
1	3	2	4	6
2	6	1	2	2
2	2	1	4	1
3	5	5	2	4
6	3	6	6	4
2	2	4	1	5
6	4	1	5	1
6	5	1	3	4
5	5	6	6	3
2	6	3	2	5
5	4	5	2	5
3	6	5	5	4
2	4	4	3	2
5	6	6	3	5
1	3	1	5	5
1	5	3	6	1
6	1	1	3	2
1	4	4	4	4
6	5	1	2	4
4	3	2	1	3
5	5	3	5	5
2	1	1	2	5
3	2	4	1	4
6	6	6	1	2
6	3	3	4	2
6	6	4	5	1
1	6	3	3	6
1	6	4	1	6
6	4	5	1	1
5	5	6	2	6
3	4	2	1	6
4	3	5	5	2
4	2	1	6	1
6	1	2	2	5
4	4	6	6	5
1	5	1	4	1
2	3	2	2	3
1	1	1	2	1
4	3	2	2	3
2	2	1	2	6
4	5	6	6	4
6	4	2	5	6
6	4	1	1	4
2	1	3	2	1
2	5	4	1	3
6	5	5	4	5
4	6	4	1	2
3	1	6	3	5
4	2	4	1	2
3	5	5	6	2
2	2	3	2	5
5	6	5	2	2
1	4	3	2	2
6	3	1	2	3
6	5	5	2	6
2	5	5	1	1
1	4	1	6	2
2	1	3	3	3
6	5	2	3	2
1	1	5	5	6
6	2	6	6	3
1	4	1	5	3
4	6	3	1	4
1	6	6	6	6
4	2	3	4	3
5	5	3	2	6
2	3	4	5	1
6	1	5	1	4
1	3	2	6	3
2	2	5	6	6
4	2	3	5	4
1	3	4	5	1
1	2	3	1	3
4	4	5	4	4
4	6	2	3	3
6	1	3	6	4
1	2	3	6	3
3	3	1	5	1
5	2	5	5	1
3	6	1	5	3
2	6	3	1	4
4	3	6	1	6
3	6	2	2	3
6	5	6	2	2
4	2	2	1	4
1	2	6	6	2
3	4	5	4	6
2	4	6	6	1
1	6	5	4	1
2	5	6	5	3
5	3	2	5	3
6	5	6	5	6
3	1	5	6	4
3	2	6	5	3
3	3	2	2	4
6	2	4	3	2
1	2	2	5	4
1	1	1	2	6
6	5	1	2	2
1	1	5	4	3
2	2	3	4	1
1	3	6	1	4
4	2	1	3	1
4	2	1	2	2
6	5	2	5	4
2	4	5	1	6
1	4	3	6	5
5	1	4	1	1
3	2	6	3	6
6	5	3	6	1
3	1	2	3	2
5	3	3	4	4
4	5	3	4	3
5	4	2	6	5
5	5	3	5	1
6	5	6	1	3
6	2	6	6	1
2	3	3	5	6
4	3	1	1	5
1	6	3	3	4
5	2	1	5	1
6	6	1	1	6
5	1	6	4	3
1	3	3	5	6
4	5	5	2	3
6	3	1	2	6
3	4	5	4	5
1	1	1	3	5
4	6	5	3	1
6	5	6	1	3
2	5	5	3	1
6	3	3	6	3
6	1	3	1	5
2	5	1	1	5
5	2	6	4	6
6	5	4	2	3
3	3	5	4	1
3	5	5	2	1
1	5	1	1	3
5	4	2	4	5
4	5	2	3	3
3	5	3	4	3
3	1	2	2	1
1	6	5	3	5
2	1	2	6	6
1	6	4	6	6
3	2	3	4	4
5	6	5	1	6
6	1	5	1	2
5	5	1	4	3
6	1	1	2	5
5	4	5	3	6
1	6	6	4	3
6	6	3	1	5
5	6	4	1	3
4	3	6	1	1
3	5	3	4	5
4	1	6	1	5
1	6	6	3	4
4	3	1	1	2
4	4	2	4	3
3	4	5	4	2
2	1	4	3	2
1	3	6	2	2
5	5	5	1	1
5	4	1	5	1
1	6	5	4	1
1	3	6	1	3
5	5	3	1	2
2	6	3	2	2
1	5	4	4	2
3	4	2	2	2
4	3	1	1	3
6	6	3	3	3
2	5	3	2	1
2	1	6	2	5
1	2	4	3	2
2	1	4	4	3
6	2	1	2	6
2	5	3	2	2
2	2	1	6	4
6	1	5	3	6
5	2	6	2	1
5	2	5	5	5
2	1	6	2	2
1	1	6	5	1
3	4	5	5	2
6	6	5	2	6
3	1	1	1	3
3	6	4	2	4
2	6	2	2	6
6	4	4	4	3
4	1	3	4	2
6	5	6	5	2
2	5	4	6	3
2	5	2	1	1
6	2	2	3	6
3	4	5	3	6
2	4	3	3	6
1	3	1	4	4
2	3	2	4	5
4	2	1	5	1
4	2	6	3	1
3	6	2	5	6
3	1	4	6	4
1	4	5	2	4
5	1	4	1	6
1	2	6	2	6
6	3	6	4	2
6	4	6	4	3
5	3	5	4	6
2	6	1	4	3
1	2	4	6	2
6	2	4	5	1
1	2	5	1	3
6	2	6	5	4
2	2	4	6	3
3	3	1	2	4
1	1	4	6	3
1	4	6	5	5
4	6	3	4	5
4	2	3	1	2
5	3	6	1	1
5	6	6	3	3
6	5	5	4	6
4	2	1	6	3
5	6	2	1	4
6	5	5	3	3
6	1	4	6	3
3	2	3	1	3
1	3	3	2	6
2	1	1	2	5
4	3	3	4	1
1	5	1	1	2
6	3	5	2	5
6	1	6	6	3
2	1	1	3	3
4	5	2	5	4
6	6	1	2	4
3	3	3	5	5
3	1	6	4	3
1	5	3	1	4
3	1	4	1	2
2	1	6	2	4
5	4	2	6	3
4	2	1	3	6
1	3	3	2	5
6	6	6	1	5
3	4	3	1	1
5	4	3	5	6
2	2	4	6	2
5	4	4	1	4
1	1	3	2	5
4	1	2	1	1
2	6	5	2	5
3	5	2	1	6
2	1	1	2	4
2	3	3	4	4
3	4	5	5	1
1	5	5	6	6
2	1	2	6	6
4	2	6	3	2
5	5	5	5	2
2	6	6	6	6
2	4	1	3	3
2	4	6	5	5
2	6	1	4	1
1	5	3	2	5
4	2	5	6	4
6	6	1	1	3
4	1	1	6	2
3	1	4	1	6
3	4	4	4	2
1	4	1	3	6
3	3	6	6	1
1	5	1	1	2
5	5	3	6	1
5	2	4	2	6
3	5	1	6	6
3	5	3	5	1
2	1	4	5	3
1	5	4	3	6
1	6	6	2	3
6	6	4	2	5
1	2	5	2	6
5	3	6	5	6
5	1	1	1	5
6	5	3	6	3
1	1	5	5	3
5	2	5	5	3
2	4	4	3	6
4	1	6	3	5
3	4	2	5	2
1	4	4	5	5
3	2	1	3	6
4	3	1	5	4
6	3	6	4	4
4	6	6	2	5
1	3	2	6	5
4	2	2	4	4
5	6	6	6	2
6	6	3	6	5
4	4	4	3	4
3	2	3	4	5
4	5	2	3	6
4	5	6	3	6
2	4	1	6	2
3	2	6	6	5
2	5	2	3	6
1	6	5	6	1
2	6	3	2	3
1	2	2	6	5
1	1	5	6	3
2	3	5	5	1
6	2	3	4	5
6	4	6	2	4
5	2	1	2	2
3	1	3	3	5
2	1	5	2	6
6	2	2	2	6
3	3	1	4	3
3	1	5	4	5
6	2	1	4	6
3	1	1	2	2
5	6	2	1	6
2	6	5	3	6
5	1	6	3	3
3	5	6	1	6
1	4	2	2	3
1	2	1	4	3
1	6	5	4	6
1	3	5	3	6
3	4	3	3	2
2	1	2	5	1
6	2	2	1	2
2	4	6	1	6
2	6	6	2	2
5	2	1	5	6
2	5	1	1	4
6	3	3	4	5
5	4	2	4	5
3	6	3	3	6
5	3	6	4	3
1	4	3	1	3
1	3	4	3	5
5	2	1	3	2
1	2	3	2	6
2	2	5	5	3
5	3	5	2	2
1	2	3	4	3
2	2	4	4	6
4	1	1	6	5
5	5	6	1	5
1	2	4	5	4
3	5	1	4	3
1	4	2	5	5
1	1	2	3	3
2	4	1	6	4
1	1	1	1	4
5	3	2	5	2
6	3	1	2	6
3	6	3	2	1
5	5	6	5	5
6	1	5	2	2
2	5	6	5	6
3	1	6	4	3
1	3	3	1	5
3	6	2	1	5
5	4	3	5	5