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# Chi Square and ANOVA

These hitter data were collected on 6-23-2004 and represent the top 50 hitters in Major League Baseball on that date.
Perform the following analyses on the data, interpret your findings and summarize what each analysis means.

1. Chi square analysis -
Do the top 50 hitters come predominantly from one or several divisions?
The Yankees and Red Sox have the highest payrolls in baseball, so we would assume that the top hitters would be from the American League East, where both of these teams reside.
Arrange the data in a 2x3 table, with the two leagues, National and American, as rows, and three divsions, West, Central, and East as columns.
The data in the table should be a count of the regions that each of the top 50 players is from.
Test the hypothesis that the hitters do not come evenly from the 6 regions.
State the critical value that you will test your Chi observed against; interpret your Chi observed. Interpret your findings.

2. ANOVA -
If you are a top 50 hitter, this usually indicates that you get up to bat often. With the designated hitter rule in the American League, you would expect hitters
to bat even more often that their National League counterparts, where the pitcher hits as well.
Test the hypothesis that the number of at-bats is different for the six divisions.
Break up the data into the six different groups (ALE, ALC, ALW, NLE, NLC, NLW) and then run the one-way ANOVA on these data.
Start by sorting the at-bat data by the League first and then Region second, which will give you six groups for the data analysis.
Put these data into six columns before running the data analysis.
Note that the sample sizes for each of the six groups should match the data that you provided for the chi square test above.
·         Is the analysis significant? What does this mean?
·         If the test is significant, run the Tukey analysis and interpret.
Player League Region Team At bats Homers
1 American West ANA 259 12
2 American West ANA 108 11
3 American West ANA 281 17
4 National West ARI 259 14
5 National West ARI 273 18
6 National East ATL 250 12
7 National East ATL 215 14
8 American East BOS 279 16
9 American East BOS 248 19
10 National Central CHC 275 14
11 National Central CHC 276 18
12 National Central CIN 232 20
13 National Central CIN 247 19
14 National Central CIN 268 13
15 American Central CLE 237 11
16 National West COL 241 16
17 National West COL 225 13
18 National West COL 248 16
19 American Central CWS 206 18
20 American Central CWS 199 13
21 American Central CWS 225 15
22 National East FLA 187 12
23 National East FLA 267 17
24 National East FLA 265 16
25 National Central HOU 249 11
26 National Central HOU 221 16
27 American Central KC 257 14
28 National West LA 264 16
29 National West LA 248 11
30 American Central MIN 256 13
31 National East MON 228 12
32 National East NYM 248 16
33 American East NYY 264 18
34 American East NYY 248 13
35 American East NYY 175 11
36 American West OAK 187 13
37 American West OAK 267 13
38 National East PHI 234 15
39 National East PHI 222 23
40 National East PHI 221 12
41 National Central PIT 253 15
42 National Central PIT 215 12
43 National West SF 153 18
44 National West SF 248 12
45 National Central STL 249 19
46 National Central STL 242 15
47 National Central STL 213 12
48 National Central STL 247 17
49 American East TB 195 12
50 American West TEX 272 17

#### Solution Summary

Chi square and ANOVA yeses are used to analyze the top hitters in the American League. The solution determines if the analysis is significant.

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