2.5 solutions

# The data are below for each season separately and for

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they were at bat (that means the number of times they attempted to make a hit.) The data are below, for each season separately and for the two seasons combined. Season 1 Season 2 Mike Matt Mike Matt Hits 5 59 Hit 80 9 At Bat 10 100 At Bat 100 10 Both seasons combined Mike Matt Hits 85 68 At Bat 110 110 13. Who was the better hitter in Season 1? Explain why. Mike hit 5 times out of 10 = 50% Matt hit 59 times out of 100 = 59%*** 14. Who was the better hitter in Season 2? Explain why. Mike hit 80 times out of 100 = 80% Matt hit 9 times out of 10 = 90%*** 15. Who was the better hitter overall (both seasons combined?) Explain why. Overall: Mike hits 85 out of 110 times = 77%*** Matt hits 68 out of 110 times = 62% 16. Is this an example of Simpson’s Paradox? If yes, explain WHY it’s occurring. If not, explain WHY NOT. Yes, it’s Simpson’s paradox. Mike hits better overall, but Matt hits better in each Season separately. Why is this? First note that both batters did better in Season 2 than Season one. Matt had fewer at bats and therefore fewer hits in Season two,so that lowered his overall hitting percentage. Mike hit more times in Season 2, and this raised his overall hitting percentage. 4
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