Greetings Dr. O!
I spend a couple days a week hanging out at the local record store, where, when Jason comes in on Tuesdays, the talk invariably is about local professional sports. Of course, this time of year, it is the Chicago Bears. Scary thought.
But Jason is a Cubs fan (the store owner John is a Sox fan). My first major league baseball game was a Sox game - my grandparents took me in 1960 after they had traded away a very good core of players to get some veterans (Earl Battey, Johnny Romano, Norm Cash, Johnny Callison), in an attempt to repeat as American League champions.
But I've attended more Cubs game.
Which is all quite irrelevant since baseball quit on its fans in 1994 and we learned that October can be survived without the world series.
But, in the present day, at the record shop, we were discussing who the Cubs will hire as manager, and also who they SHOULD hire.
Before Lou Pinella retired, the Cubs record was: 51-74 winning % = 40.800%
Under Pinella's replacement, the Cubs record was: 24-13 winning % = 64.865%
2010 Cubs record was 75-87 winning % = 46.296
My formulation of the null hypothesis is this:
Ho: Cubs probability of winning was the same under both Pinella and his replacement
Confidence interval: 90%
let P1 , the probability of the cubs winning game = .46296
then for the 125 games the Cubs played under Pinella, the expected number of victories =
.46296 * 125 = 57.87
And the standard deviation = sqrt (N*p*q) = sqrt(125*.469296*(1-.46296) =
sqrt(31.1325108) = 5.58
37*.46296 = 17.13
std dev = sqrt(37*.469296*(1-.469296)) = 3.04
In fact, under Pinella, the cubs won 51 games (1 std deviation below the expected 57), and under new-manager guy, won 23, (2 std deviations above the expected 17)
Thus P2 is not equal to P1 at better than a 90% confidence level.
KEEP THE NEW GUY AS MANAGER FOR 2011 SEASON !!
Well, at least the Cubs did the right thing, for WHATEVER reason!!
Your student and admirerer forever,
MarKUSSaurusREX
(because I don't SKYPE)
Mark Ganzer
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