Reference no: EM132171272
Problem - The ESPN Home Run Tracker computes a variety of measurements for every home run hit in Major League Baseball, including true distance, speed of bat, elevation angle and apex. Independent random samples of home runs during the 2013 season were obtained from four different ballparks, and the distance was recorded for each. The summary statistics are given in the following table.
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Ballparks
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Fenway Park
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Coors Field
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Dodger Stadium
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Rogers Centre
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|
n
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20
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20
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20
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20
|
|
x
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395.90
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411.55
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397.80
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400.10
|
|
s
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16.14
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21.60
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20.85
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28.38
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a) Is the constant standard deviation assumption valid in this case? Please explain your answer.
b) Fill in the following ANOVA table given the information below. Remember work is required for each ungreyed box in the table
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Source of Variation
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Degrees of freedom
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Sum of squares
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Mean square
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F
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Factor
|
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2958
|
|
|
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Error
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|
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461.7
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|
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Total
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|
|
|
|
c) Assuming that the populations are normal, is there any evidence to suggest that the average home-run distances in at least two of the ballparks are different? Use a 0.05 Perform the complete four-step summary. Be sure to include the two degrees of freedom necessary to calculate the p-value. To calculate the p-value, either find an online source, use R, or your graphing calculator. You may use the numbers calculated above in part b), without re showing your work.
d) Construct the Tukey 95% confidence intervals to isolate the pairs of means contributing to the overall difference. For each pair indicate whether the two means are different or not.
e) Draw a diagram to represent the results of the multiple comparison procedure in part d).
f) If someone asks which of these ballparks has the longest average home-run distance how would you respond? Explain your answer.