Western University has only one women's softball scholarship remaining for the coming year. The final two players that Western is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually in for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player's batting performance in their junior and senior years of high school are as follows: Excel File: data02-51.xlsx Outcome Hit No Hit Allison Fealey Junior Outcome 15 Hit Senior 75 Outcome 175 Hit No Hit Allison Fealey Emily Janson Which player should be awarded the scholarship? Explain. 25 85 Total At-Bats 40 250 Total At-Bats 200 120 A player's batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal. a. Calculate the batting average for each player in her junior year. Junior Allison Fealey 0.375 Emily Janson 0.35 Calculate the batting average of each player in her senior year. Senior 0.3 0.292 Emily Janson No Hit Total At-Bats Calculate each player's batting average for the combined two years. Junior/Senior Years Junior Allison Fealey Emily Janson Which player should be awarded the scholarship? Explain. 70 Since her batting average for both junior and senior years was higher, Allison Fealey b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows: Combined 2-Year Batting A. Fealey E. Janson Senior 130 35 ✓should be awarded the scholarship. Because - Select your answer has the higher combined batting average, she should be awarded the scholarship. c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies. - Select your answer.
Western University has only one women's softball scholarship remaining for the coming year. The final two players that Western is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually in for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player's batting performance in their junior and senior years of high school are as follows: Excel File: data02-51.xlsx Outcome Hit No Hit Allison Fealey Junior Outcome 15 Hit Senior 75 Outcome 175 Hit No Hit Allison Fealey Emily Janson Which player should be awarded the scholarship? Explain. 25 85 Total At-Bats 40 250 Total At-Bats 200 120 A player's batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal. a. Calculate the batting average for each player in her junior year. Junior Allison Fealey 0.375 Emily Janson 0.35 Calculate the batting average of each player in her senior year. Senior 0.3 0.292 Emily Janson No Hit Total At-Bats Calculate each player's batting average for the combined two years. Junior/Senior Years Junior Allison Fealey Emily Janson Which player should be awarded the scholarship? Explain. 70 Since her batting average for both junior and senior years was higher, Allison Fealey b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows: Combined 2-Year Batting A. Fealey E. Janson Senior 130 35 ✓should be awarded the scholarship. Because - Select your answer has the higher combined batting average, she should be awarded the scholarship. c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies. - Select your answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Batting Average Comparison for Scholarship Decision**
*Introduction:*
Western University has one women's softball scholarship available for the upcoming year. The candidates are Allison Fealey and Emily Janson. Their speed and defensive skills are almost identical, so the decision will be based on who has the better batting average from their junior and senior years in high school.
*Data Summary:*
Each player's batting performance is presented as follows:
- **Allison Fealey**
- Junior Year:
- Hits: 75
- Total At-Bats: 200
- Senior Year:
- Hits: 15
- Total At-Bats: 50
- **Emily Janson**
- Junior Year:
- Hits: 70
- Total At-Bats: 200
- Senior Year:
- Hits: 35
- Total At-Bats: 120
*Calculation of Batting Averages:*
- Junior Year Batting Averages:
- Allison Fealey: 0.375
- Emily Janson: 0.350
- Senior Year Batting Averages:
- Allison Fealey: 0.300
- Emily Janson: 0.292
*Scholarship Recommendation:*
Since both junior and senior batting averages of Allison Fealey were higher, it is recommended that she should be awarded the scholarship.
*Combined 2-Year Batting:*
Data should be aggregated into a combined 2-year crosstabulation:
- **Combined Hits and At-Bats:**
- Allison Fealey:
- Hits: 90
- Total At-Bats: 250
- Emily Janson:
- Hits: 105
- Total At-Bats: 320
- Combined Year Batting Averages:
- Allison Fealey: 0.360
- Emily Janson: 0.328
*Final Scholarship Decision:*
Based on the combined batting averages, Allison Fealey has a higher average and should be awarded the scholarship.
*Conclusion:*
The recommendations from parts (a) and (b) are consistent. Allison Fealey maintains a superior batting average across all comparisons.
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