potential savings offered by Diehard, but is also concerned about the quality of the dice produced by the new supplier. EWI has a reputation for high integrity, and its management feels that it is imperative that the dice included with Bunco Wa
Everybody Wins Inc.: Everybody Wins Inc. (EWI) manufactures and sells several different board games online and through department stores nationwide. EWI's most popular game, Bunco Wars, is played with 5 six-sided dice. EWI has purchased dice for this game Gameplay Ltd. for twenty-five years, but the company is now considering a move to Diehard, Inc., a new supplier that has offered to sell dice to EWI at a substantially lower price. EWI management is intrigued by the potential savings offered by Diehard, but is also concerned about the quality of the dice produced by the new supplier. EWI has a reputation for high integrity, and its management feels that it is imperative that the dice included with Bunco Wars are fair.
To alleviate concerns about the quality of the dice it produces, Diehard allows EWI's manager of product quality to randomly sample five dice from its most recent production run. While being observed by several members of the Diehard management team, EWI'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 attached data file Diehard.
EWI 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?
Prepare a report that addresses the following:
a. Use
b. Based on these descriptive statistics, what are your preliminary conclusions about the fairness of the five selected dice?
c. Use the data collected by EWI'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 significance level (alpha) of 0.01.
d. Do the results of your hypothesis tests provide evidence that Diehard is producing unfair dice? Why or why not?
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