Statistics Solutions

Solution: There is an ongoing argument about which of three Fraternities—Sigma, Epsilon, and Rho— is better at winning charity competitions. Sigma argues

Question: There is an ongoing argument about which of three Fraternities—Sigma, Epsilon, and Rho— is better at winning charity competitions. Sigma argues that not all fraternities are equally competitive and skilled. They think their members are better at winning competitions compared to Epsilon and Rho. Sigma hires an independent marketing firm to carry out a small research project to confirm their hypothesis (i.e., "all three fraternities are not equal at winning charity competitions"). The marketing firm collected a sample of individuals who are members of one of the three fraternities. The data are as follows:

Customer Frat Number of Charity Competition Wins
Ari Epsilon 3
Fred Epsilon 0
Nicole Epsilon 4
Shaun Epsilon 3
Lisa Rho 1
Shaina Rho 1
Crosby Rho 3
Laina Rho 4
Priscilla Sigma 4
Rocky Sigma 10
Penny Sigma 5
Jules Sigma 7

Is Sigma’s hypothesis correct? That is, are the three fraternities not equal at winning charity competitions (assume that "Number of Charity Competition Wins" is a good measure of this)? Be sure to show ALL work and EXPLAIN your results. What are the null and alternative hypotheses? Please ignore the small sample size and any big ratios of variances across groups.

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