4. a. The following two-way table compares Derek Jeter and David Justice in 1995: 1995 Derek Jeter David Justice Hits 12 104 Misses 36 307 Which player was better in 1995? (5 points) b. Here are their numbers from 1996: 1996 Derek Jeter David Justice Hits 183 45 Misses 399 95 Which player was better in 1996? (5 points) c. Here are their numbers from 1997: 1997 Derek Jeter David Justice Hits 190 163 Misses 464 332 Which player was better in 1997? (5 points) d. Construct a two-way table showing their numbers during the three years 1995-1997 (5 points) 1995-1997 Hits Misses Derek Jeter David Justice f. Which player was better during the three years combined? (5 points)
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Simpson's Paradox, Jeter -vs- Justice: In baseball, the batting average (BA) is defined as the quotient of hits divided by the times at bat. Below is a table for the 1995 and 1996 batting averages for Derek Jeter and David Justice. Who has the better batting average? Try a straight average of the two years and a weighted average based on the number of times at bat. You should get contradictory results. Player BA - 1995 BA - 1996 Derek Jeter .250 (48 times at bat) .314 (582 times at bat) David Justice .253 (411 times at bat) .321 (140 times at bat) (a) Looking within each category of year, which player had a better batting average? (b) Using a weighted average across both years, calculate the mean batting average for each player. Which player had a better batting average? (c) Why did Derek Jeter fair so well using the weighted average?
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14. The Major League Baseball career and single-season home run records are held by Barry Bonds of the San Francisco Giants. Here are Bonds's annual home run totals from 1986 (his first year) through 2007 (his last year): 16 37 25 33 45 24 19 33 25 34 34 46 73 42 40 37 49 46 45 5 26 28 (a) Make a stemplot of the data. Are there any outliers? (b) Find his career mean and median number of home runs. How do these change when you drop his 2001 season total of 73? What general fact about the mean and median does your result illustrate?
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