Question: Baseball has always been a favorite pastime in America, and is rife with statistics and theories. While baseball purists may disagree, to an applied statistician no topic in baseball is too small or hypothesis too unlikely. In a recent paper, researchers at Wayne State University showed that major-league players who have nicknames live 21/2 years longer than those without them (The Wall Street Journal, July 16, 2009). You do not believe in this result and decide to conduct a test to prove it wrong. Consider the following data on the lifespan o f a player and the nickname variable, which equals 1 if the player had a nickname and 0 otherwise. These data can also be found on the text website, labeled Nicknames.
a. Create two subsamples consisting of players with and without nicknames. Calculate the average longevity for each subsample.
b. Specify the hypotheses to contradict the claim made by researchers at Wayne State University.
c. State the conclusion of the test using a 5% level of significance. Assume the population variances are unknown but equal.
d. What assumptions did you make regarding the populations?