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Hypothesis Test

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Submitted By fermussolini
Words 362
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Math 1150
April 18, 2012
Hypothesis Test
Barry Bonds Analysis
For the analysis of Mr. Bonds, we need to define the years of alleged drug use and pick a suitable statistic. Mr. Bonds has been accused of using performance-enhancing drugs at the end of 1998. Mr. Bonds only participated in 14 games in 2005 due to various factors. This disruption in the normal process provides a good place to break after the alleged drug use.
The key performance metric for batters tends to be their Batting Average (BA). Mr. Bonds’ batting average from 1986 to 1998 is .289, and his average from 1999 to 2004 is .329. Since a larger batting average is better, Mr. Bonds’ average BA did improve in the alleged drug-use years. However, is the difference in his Batting Average due to random variation, or is it large enough to say that he actually improved? The hypothesis test for Mr. Bonds would be:
H0: Mr. Bonds’ average BA was the same before and after
H1: Mr. Bonds’ average BA was different after alleged drug use

The chances of getting it wrong (probability of a Type I Error) using the available statistics and it came out to 3%. Put another way, if we conclude that Mr. Bonds’ average BA is different during the period of alleged drug use, then we would be wrong only 3 times in 100. As I said before, we typically would like the chance of getting it wrong to be less than 5% to conclude the averages are different. In this case, the chance of getting it wrong is less than 5%, so I would conclude that Mr. Bonds’ average BA did improve after 1998. This difference in average can be seen visually in the dot plot below. The blue dots represent Mr. Bonds’ Batting Average before alleged drug use, and the green triangles represent Mr. Bonds’ BA after alleged drug use. Visually, it appears that the average did increase after 1998. The formal calculation of the Type I error tells us that what we see on the dot plot is in fact a shift in the mean and not just random variation.

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