We have a (made up, sadly) set of data on number of bases stolen this year from each of the 30 teams in Major League Baseball. Over the past 50...

We have a (made up, sadly) set of data on number of bases stolen this year from each of the 30 teams in Major League Baseball. Over the past 50 years, the average team steals 88 bases in a year. We want to know if the mean baseball team stole significantly more bases than usual last year.

a) Is this a one or two-sided test? Explain.

b) Is there evidence, at the alpha = 0.05 that the mean stolen bases (per team this year) is more than 88? What information did you use to make this conclusion.

c) Is there evidence, at the alpha = 0.05 that the mean stolen bases (per team this year) is LESS than 88? What information did you use to make this conclusion.

d) Summarize why your answers for parts B and C differ even though they are both one-sided tests on the same data from the same hypothesized mean?

**Added note for interest: The 30 teams are not a simple random sample in the classical sense, because there are only 30 teams. However, you can imagine that last year's baseball season was the result of random chance, much like the roll of some dice. In that case, what we observe a sample of all possible seasons that could have happened. When we do hypothesis tests, we're really asking “could something like this have happened by chance, or is there so other reason that we see this trend?”