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# Applying ANOVA to a data set

Refer to the Baseball data set, which reports information on the 30 Major League Baseball teams for the 2002 season.

a.At the 0.10 significance level is there a difference in the variation in team salary among the American and National League teams? Explain

b.Create a variable that classifies a team's total attendance into three groups: less than 2.0 million, 2.0 up to 3.0 million, and 3.0 or more. At the 0.01 significance level is there a difference in the mean number of games won among the three groups? Explain

c. Using the same attendance variable developed in part (b) is there a difference in the mean team batting average? Use the 0.01 significance level. Explain

d. Using the same attendance variable used in part (b) is there a difference in the mean salary of the group? Use the 0.01 significance level. Explain

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15

Team League Built Size Surface Salary Salary -mil Wins Attendance Batting ERA HR Error SB Year Average
Boston 1 1912 33871 0 123505125.0 123.5 95.0 2,847,798 0.281 4.74 199 109 45 1989 512,930
New York Yankees 1 1923 57746 0 208306817.0 208.3 95.0 4,090,440 0.276 4.52 229 95 84 1990 578,930
Oakland 1 1966 43662 0 55425762.0 55.4 88.0 2,108,818 0.262 3.69 155 88 31 1991 891,188
Baltimore 1 1992 48262 0 73914333.0 73.9 74.0 2,623,904 0.269 4.56 189 107 83 1992 1,084,408
Los Angles Angels 1 1966 45050 0 97725322.0 97.7 95.0 3,404,636 0.270 3.68 147 87 161 1993 1,120,254
Cleveland 1 1994 43368 0 41502500.0 41.5 93.0 2,014,220 0.271 3.61 207 106 62 1994 1,188,679
Chicago White Sox 1 1991 44321 0 75178000.0 75.2 99.0 2,342,804 0.262 3.61 200 94 137 1995 1,071,029
Toronto 1 1989 50516 1 45719500.0 45.7 80.0 2,014,995 0.265 4.06 136 95 72 1996 1,176,967
Minnesota 1 1982 48678 1 56186000.0 56.2 83.0 2,034,243 0.259 3.71 134 102 102 1997 1,383,578
Tampa Bay 1 1990 44027 1 29679067.0 29.7 67.0 1,141,915 0.274 5.39 157 124 151 1998 1,441,406
Texas 1 1994 52000 0 55849000.0 55.8 79.0 2,525,259 0.267 4.96 260 108 67 1999 1,720,050
Detroit 1 2000 40000 0 69092000.0 69.1 71.0 2,024,505 0.272 4.51 168 110 66 2000 1,988,034
Seattle 1 1999 45611 0 87754334.0 87.8 69.0 2,724,859 0.256 4.49 130 86 102 2001 2,264,403
Kansas City 1 1973 40529 0 36881000.0 36.9 56.0 1,371,181 0.263 5.49 126 125 53 2002 2,383,235
Atlanta 0 1993 50062 0 86457302.0 86.5 90.0 2,520,904 0.265 3.98 184 86 92 2003 2,555,476
Arizona 0 1998 49075 0 62329166.0 62.3 77.0 2,059,327 0.256 4.84 191 94 67 2004 2,486,609
Houston 0 2000 42000 0 76799000.0 76.8 89.0 2,805,060 0.256 3.51 161 89 115 2005 2,632,655
Cincinnati 0 2003 42,059 0 61892583.0 61.9 73.0 1,923,254 0.261 5.15 222 104 72
New York Mets 0 1964 55775 0 101305821.0 101.3 83.0 2,827,549 0.258 3.76 175 106 153
Pittsburgh 0 2001 38127 0 38133000.0 38.1 67.0 1,817,245 0.259 4.42 139 117 73
Los Angeles Dodgers 0 1962 56000 0 83039000.0 83.0 71.0 3,603,680 0.253 4.38 149 106 58
San Diego 0 2004 42,445 0 63290833.0 63.3 82.0 2,869,787 0.257 4.13 130 109 99
Washington 0 1961 56000 0 48581500.0 48.6 81.0 2,730,352 0.252 3.87 117 92 45
San Francisco 0 2000 40800 0 90199500.0 90.2 75.0 3,181,020 0.261 4.33 128 90 71
St Louis 0 1966 49625 0 92106833.0 92.1 100.0 3,542,271 0.270 3.49 170 100 83
Florida 0 1987 42531 0 60408834.0 60.4 83.0 1,852,608 0.272 4.16 128 103 96
Philadelphia 0 2004 43500 0 95522000.0 95.5 88.0 2,665,304 0.270 4.21 167 90 116
Milwaukee 0 2001 42400 0 39934833.0 39.9 81.0 2,211,323 0.259 3.97 175 119 79
Chicago Cubs 0 1914 38957 0 87032933.0 87.0 79.0 3,100,092 0.270 4.19 194 101 65
Colorado 0 1995 50381 0 48155000.0 48.2 67.0 1,914,385 0.267 5.13 150 118 65

#### Solution Preview

a. At the 0.10 significance level is there a difference in the variation in team salary among the American and National League teams? Explain

Hypotheses:
Null Hypothesis:
Verbal Hypothesis:
H0: there is no difference in the variation in team salary among the American and National League teams
Numerical hypothesis:
H0:

Alternative Hypothesis:
Verbal Hypothesis:
H0: there is a difference in the variation in team salary among the American and National League teams
Numerical hypothesis:
Ha: (two -tailed test)
Step 2:
Level of Significance:
α = 0.10
Step 3:
Decision Rule:
If the p value for the test statistic is greater than the given level of significance we may accept the null hypothesis otherwise reject the null hypothesis.
Step 4:
Test Statistic:
Since the sample size is 30, we can use the Small sample test "t-test" to test the difference between the two means. The test statistic is given below:

t =

By using Megastat

Hypothesis test  Compare two independent groups

Hypothesis Test: Independent Groups (t-test, pooled variance)

Hypothesis Test: Independent Groups (t-test, pooled variance)

Salary -mil Group 2
75.480 70.949 mean
45.931 20.669 std. dev.
14 16 n

28 df
4.5307 difference (Salary -mil - Group 2)
1,208.3468 pooled variance
34.7613 pooled std. dev.
12.7213 standard error of difference
0 hypothesized difference

0.36 t
.7244 p-value (two-tailed)

Thus the value of test statistic is t = 0.36
Step 5:
Conclusion:

Since the p value of test statistic't' is greater than 0.10 level of significance there is no ...

#### Solution Summary

Applying ANOVA analysis to baseball data set is examined. The differences in the mean salary of the players are determined.

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