Concept explainers
(a)
To make: a two-way table of player versus outcome
(a)
Answer to Problem 34E
Outcomes | |||
Players | Hit | No Hit | |
Joe | |||
Moe |
Explanation of Solution
Given:
Player | Pitcher | Hits | At-bats |
Joe | Right Left | ||
Moe | Right Left |
Calculation:
We have a data on the performance of two players Joe and Moe against right-handed and left-handed pitchers.
As per the requirement, consider the above given table with no hits where no hits is the value obtained by subtracting the number of hits from the number of at-bats.
Player | Pitcher | Hits | AT-bats | No Hits |
Joe | Right | |||
Left | ||||
Moe | Right | |||
Left |
Using above table, we construct a two-way table of player(Joe or Moe) versus outcome(hit or no hit).
Outcomes | |||
Players | Hit | No Hit | |
Joe | |||
Moe |
Conclusion:
Therefore, the two-way table is drawn.
(b)
To show: Simpson’s paradox holds:
(b)
Answer to Problem 34E
The given illustration holds Simpson’s paradox.
Explanation of Solution
Here Moe’s overall batting average is good(
For left pitchers Joe faced for
By definitions, the proportion of hits for Joe in left pitcher is given as
By definitions, the proportion of hits for Moe in left pitcher is given as
For left pitchers we observed that Joe has given
The Simpson’s Paradox says that sometimes as association between two categorical variables gets reversed when we consider third variable. From the above we observed that the Moe’s batting average is good, as we consider both the pitchers combined but the Joe’s batting average is good, as we consider both the pitchers individually. Therefore the given illustration holds Simpson’s paradox.
Conclusion:
Therefore the given illustration holds Simpson’s paradox.
(c)
To explain: why the given scenario happens to Joe and Moe.
(c)
Answer to Problem 34E
This could have happened because Joe has faced left pitcher
Explanation of Solution
Calculation:
The manager doesn’t believe that one Joe can hit better against both left-handed and right-handed yet have overall lower batting score. The data is shown below:
Player | Pitcher | Hits | AT-bats | |
Joe | Right | |||
Left | ||||
Moe | Right | |||
Left |
This could have happened because Joe has faced left pitcher
Joe’s Right handed Hits
Therefore, Joe has lower average score is that he has faced left pitcher
Conclusion:
Therefore, Joe has lower average score is that he has faced left pitcher
Chapter 1 Solutions
The Practice of Statistics for AP - 4th Edition
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