Assume the table gives data on field goal shooting for two members of the Benedict College 2014-2020 men's basketball team. Seth Fitzgerald Roberto Mantovani Made Missed Made Missed Two-pointers 123 118 87 84 Three-pointers 31 6 2 17 NOTE: The numerical values in this problem have been modified for testing purposes. (a) What percent of all field goal attempts did Seth Fiqzgerald make? (Enter your answers rounded to two decimal places.) Seth Fitzgerald's overall field goal percentage:_______ What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) Roberto Mantovani's overall field goal percentage:______________. (b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.) Seth Fitzgerald's two-pointers: ______________% Roberto Mantovani's two-pointers:___________ % Seth Fitzgerald's three-pointers:____________ Roberto Mantovani's three-pointers:__________ (c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation. i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group. ii) The sample size is too small and this explains why the results seem contradictory. iii) You should never compare percentages for two different groups. iv) This is an example of correlation. The comparison that holds for both field goal groups is reversed when the groups are combined into one group.

Answer:

(a) What percent of all field goal attempts did Seth Fitzgerald make? (Enter your answers rounded to two decimal places.)

Seth Fitzgerald's overall field goal percentage:__59.69%_____

What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.)

Roberto Mantovani's overall field goal percentage: ______40.31%________.

(b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.)

Seth Fitzgerald's two-pointers: _____58.57%_________%

Roberto Mantovani's two-pointers:_____41.43%______ %

Seth Fitzgerald's three-pointers:_____64.58%_______

Roberto Mantovani's three-pointers:_____35.42%_____

(c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation.

i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group

Step-by-step explanation:

a) Data and Calculations:

Benedict College 2014-2020 men's basketball team:

                               Seth Fitzgerald   Roberto Mantovani        Total

                               Made  Missed        Made   Missed       Made    Missed

Two-pointers          123         118              87           84           210        205

Three-pointers         31            6              17              2            48             8

Total                       154         124           104            86          258        210

a) All field goal attempts = 258 (154 + 104)

Field goal attempts by Seth Fitzgerald = 154/258 * 100 = 59.69%

Goal 154 - 124 = 30/258 * 100 = 11.63%

Roberto Mantovani = 104/258*100 = 40.31%

Goal 104 - 86 = 18/258 *100 = 6.98%

Percent of all two-point field goals and all three-point field goals that both Seth and Roberto made:

Goals by both = 48 (30 + 18) = 48/258*100 = 18.61 (11.63 + 6.98)

Seth Fitzgerald's two-pointers = 123/210*100 = 58.57%

Roberto Mantovani's two-pointers = 87/210*100 = 41.43%

Seth Fitzgerald's three-pointers = 31/48*100 = 64.58%

Roberto Mantovani's three-pointers = 17/48*100 = 35.42%

b) Simpson's paradox, also called Yule-Simpson effect, says that when we combine all of the groups together (e.g. two-pointer and three-pointer games played by Seth and Roberto respectively) and look at the data in total form, the correlation that we noticed before may reverse itself.  The cause of this reversion is lurking variables or numerical values of the data.

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