Refer to the Baseball 2010 data (website for data at bottom of question), which
ID: 2932529 • Letter: R
Question
Refer to the Baseball 2010 data (website for data at bottom of question), which report information on the 30 Major League Baseball teams for the 2010 season.
A. At the .05 significance level, can we conclude that there is a difference in the mean payroll of teams in the American League versus teams in the National League?
B. At the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American League versus teams in the National League?
C. Compute the mean and the standard deviation of the number of wins for the 10 teams with the highest payrolls. Do the same for the 10 teams with the lowest payrolls. At the .05 significance level, is there a difference in the mean number of wins for the two groups?
I am not convinced I answered this correctly. For each of them in my calculations, the p-value is greater than significance level and they all do not reject the null. Data set for Baseball 2010 is found at http://highered.mheducation.com/sites/0073521477/student_view0/data_sets.html.
Explanation / Answer
Refer to the Baseball 2010 data (website for data at bottom of question), which report information on the 30 Major League Baseball teams for the 2010 season.
A. At the .05 significance level, can we conclude that there is a difference in the mean payroll of teams in the American League versus teams in the National League?
We have to test the hypothesis that,
H0 : mu1 = mu2 Vs H1 : mu1 not= mu2
where mu1 and mu2 are two population mean payroll of teams in the American League and teams in the National League.
Assume alpha = level of significance = 5% = 0.05
NOw here sample data is given so we use two sample t-test assuming equal variances.
The test statistic follows t-distribution.
We can do two sample t-test in MINITAB.
steps :
ENTER data into MINITAB sheet --> STAT --> Basic Statistics --> 2-sample t --> Samples in one column --> Samples : Select payroll data --> Subscripts : Select league column --> Assume equal variances --> Options --> Confidence level : 95.0 --> Test mean : 0.0 --> Alternative : not equal --> ok --> ok
Two-Sample T-Test and CI: X12, X2
Two-sample T for X12
X2 N Mean StDev SE Mean
AL 14 97.0 43.7 12
NL 16 85.8 33.3 8.3
Difference = mu (AL) - mu (NL)
Estimate for difference: 11.2
95% CI for difference: (-17.7, 40.1)
T-Test of difference = 0 (vs not =): T-Value = 0.80 P-Value = 0.433 DF = 28
Both use Pooled StDev = 38.5
Test statistic = 0.80
P-value = 0.433
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that there is a difference in the mean payroll of teams in the American League versus teams in the National League.
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B. At the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American League versus teams in the National League?
Now similarly we have to test,
H0 : mu1 = mu2 Vs H1 : mu1 not= mu2
where mu1 and mu2 are two population means home home attendance of teams in the American League and teams in the National League
NOw here sample data is given so we use two sample t-test assuming equal variances.
The test statistic follows t-distribution.
We can do two sample t-test in MINITAB.
steps :
ENTER data into MINITAB sheet --> STAT --> Basic Statistics --> 2-sample t --> Samples in one column --> Samples : Select attendance data --> Subscripts : Select league column --> Assume equal variances --> Options --> Confidence level : 95.0 --> Test mean : 0.0 --> Alternative : not equal --> ok --> ok
Two-Sample T-Test and CI: X11, X2
Two-sample T for X11
X2 N Mean StDev SE Mean
AL 14 2.298 0.767 0.20
NL 16 2.556 0.662 0.17
Difference = mu (AL) - mu (NL)
Estimate for difference: -0.258
95% CI for difference: (-0.793, 0.276)
T-Test of difference = 0 (vs not =): T-Value = -0.99 P-Value = 0.330 DF = 28
Both use Pooled StDev = 0.713
Test statistic = -0.99
P-value = 0.330
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that there is a difference in the mean home attendance of teams in the American League versus teams in the National League.
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