Euchre One of the authors and some statistician friends have an ongoing series o

Question

Euchre One of the authors and some statistician friends have an ongoing series of Euchre games that will stop when one of the two teams is deemed to be statistically significantly better than the other team. Euchre is a card game and each game results in a win for one team and a loss for the other. Only two teams are competing in this series, which we'l call team 1 and team 2 (a) Define the parameter of interest. p = the proportion of all possible games that team 1 loses. P = number of games that team 1 plays. p = number of games that team 2 plays. pthe proportion of all possible games that team 2 loses. PE p the proportion of all possible games that team 1 wins. (b) What are the null and alternative hypotheses if the goal is to determine if either team is statistically significantly better than the other at winning Euchre?

Explanation / Answer

a) The parameter will be the proportion of games the team 1 wins as we need to determine which team is statistically significantly better and not worse

b) The null hypothesis is H(0) = proportion of games won by team 1 = 50%

Alternative hypothesis that proportion of games won by team 1 is not equal to 50%

c)The sample statistic is the proportion of games played so far that team 1 has won

d) For a stistical test to be applied a minimum number of observations say n = 10 has to made, Thus, no a winner cannot be determined in 1 or 2 games

3) a significance level of 1% will make the game last longer, because it means that we need a tighter interval for the p value and thus more number of games to make sure that team 1 or team 2 is the statistically significant team

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