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 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: 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. Then calculate the batting average of each player in her senior year. Using this analysis, which player should be awarded the scholarship? Explain.
b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows:
Calculate each player’s batting average for the combined two years. Using this analysis, which player should be awarded the scholarship? Explain.
c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.