Suppose a university has only one women's softball scholarship remaining for the coming year. The final two players that the university is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical 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. Outcome Allison Fealey Junior Senior Hit 15 80 No Hit 25 175 Total At-Bats 40 255 Outcome Emily Janson Junior Senior Hit 75 35 No Hit 130 85 Total At-Bats 205 120 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. (Round your answers to three decimal places.) (a) Calculate the batting average for each player in her junior year. Allison Fealey Emily Janson Calculate the batting average of each player in her senior year. Allison Fealey Emily Janson Using this analysis, which player should be awarded the scholarship? Explain. Because ---Select--- Allison Fealey Emily Janson had the higher batting average in both her junior year and senior year, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer. (b) Combine or aggregate the data for the junior and senior years into one crosstabulation. Outcome Player Fealey Janson Hit No Hit Total At-Bats Calculate each player's batting average for the combined two years. (Round your answers to three decimal places.) Allison Fealey Emily Janson Using this analysis, which player should be awarded the scholarship? Explain. Because ---Select--- Allison Fealey Emily Janson has the higher batting average over the combined junior and senior years, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer. (c) Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies. The recommendations in parts (a) and (b) ---Select--- are are not consistent. This is an example of ---Select--- conclusions paradox crosstabulation rule aggregation rule Simpson's Paradox . It shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be ---Select--- the same reversed when the crosstabulations are grouped or aggregated.
Suppose a university has only one women's softball scholarship remaining for the coming year. The final two players that the university is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical 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. Outcome Allison Fealey Junior Senior Hit 15 80 No Hit 25 175 Total At-Bats 40 255 Outcome Emily Janson Junior Senior Hit 75 35 No Hit 130 85 Total At-Bats 205 120 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. (Round your answers to three decimal places.) (a) Calculate the batting average for each player in her junior year. Allison Fealey Emily Janson Calculate the batting average of each player in her senior year. Allison Fealey Emily Janson Using this analysis, which player should be awarded the scholarship? Explain. Because ---Select--- Allison Fealey Emily Janson had the higher batting average in both her junior year and senior year, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer. (b) Combine or aggregate the data for the junior and senior years into one crosstabulation. Outcome Player Fealey Janson Hit No Hit Total At-Bats Calculate each player's batting average for the combined two years. (Round your answers to three decimal places.) Allison Fealey Emily Janson Using this analysis, which player should be awarded the scholarship? Explain. Because ---Select--- Allison Fealey Emily Janson has the higher batting average over the combined junior and senior years, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer. (c) Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies. The recommendations in parts (a) and (b) ---Select--- are are not consistent. This is an example of ---Select--- conclusions paradox crosstabulation rule aggregation rule Simpson's Paradox . It shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be ---Select--- the same reversed when the crosstabulations are grouped or aggregated.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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Suppose a university has only one women's softball scholarship remaining for the coming year. The final two players that the university is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical 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.
| Outcome | Allison Fealey | |
|---|---|---|
| Junior | Senior | |
| Hit | 15 | 80 |
| No Hit | 25 | 175 |
| Total At-Bats | 40 | 255 |
| Outcome | Emily Janson | |
|---|---|---|
| Junior | Senior | |
| Hit | 75 | 35 |
| No Hit | 130 | 85 |
| Total At-Bats | 205 | 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. (Round your answers to three decimal places.)
(a)
Calculate the batting average for each player in her junior year.
Allison Fealey Emily Janson
Calculate the batting average of each player in her senior year.
Allison Fealey Emily Janson
Using this analysis, which player should be awarded the scholarship? Explain.
Because ---Select--- Allison Fealey Emily Janson had the higher batting average in both her junior year and senior year, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer.
(b)
Combine or aggregate the data for the junior and senior years into one crosstabulation.
| Outcome | Player | |
|---|---|---|
| Fealey | Janson | |
| Hit | ||
| No Hit | ||
| Total At-Bats |
Calculate each player's batting average for the combined two years. (Round your answers to three decimal places.)
Allison Fealey Emily Janson
Using this analysis, which player should be awarded the scholarship? Explain.
Because ---Select--- Allison Fealey Emily Janson has the higher batting average over the combined junior and senior years, ---Select--- Allison Fealey Emily Janson should receive the scholarship offer.
(c)
Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.
The recommendations in parts (a) and (b) ---Select--- are are not consistent. This is an example of ---Select--- conclusions paradox crosstabulation rule aggregation rule Simpson's Paradox . It shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be ---Select--- the same reversed when the crosstabulations are grouped or aggregated.
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