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15 Mar 2021, 07:00
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Difficulty:
45%
(medium)
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70% (01:54) correct
30%
(02:08)
wrong
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Ten years after graduation, men and women who had participated in the Thompson High School basketball program were surveyed with regard to their individual playing records for their teams. Some of the results of the survey were curious. Seventy-five percent of those responding reported that they had started for their respective boys’ or girls’ teams, when the actual number of boys and girls who had started for their teams was only 50%.
Which one of the following provides the most helpful explanation for the apparent contradiction in these survey results?
(A) A very small number of those responding were incorrect in reporting that they held starting positions.
(B) A disproportionately high number of players who started for their teams responded to the survey.
(C) Not all starting players responded to the survey.
(D) Almost all men and women who played basketball for Thompson High School ten years earlier responded to the survey.
(E) Not all good basketball players started for their teams; some good players were deliberately held out to play later in the game.
Which one of the following provides the most helpful explanation for the apparent contradiction in these survey results?
(A) A very small number of those responding were incorrect in reporting that they held starting positions.
(B) A disproportionately high number of players who started for their teams responded to the survey.
(C) Not all starting players responded to the survey.
(D) Almost all men and women who played basketball for Thompson High School ten years earlier responded to the survey.
(E) Not all good basketball players started for their teams; some good players were deliberately held out to play later in the game.
22 Mar 2021, 05:15
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Official Explanation
If all of the men and women who had played basketball for Thompson High School ten years earlier had responded to the survey, then the results would indeed contradict the facts. However, if a disproportionately higher number of starting players responded to the survey, then the apparent contradiction can be easily explained. If only four people responded to the survey and three of them were in fact starting players, then 75% of those responding were starters. This would explain the apparent contradiction. The answer is Selection (B).
Selection (A) does not explain the contradiction; in fact, it seems to support the contradiction because it states that people reported their starting positions correctly. If instead Selection (A) had indicated that people’s faulty memories accounted for inaccurate responses, then it would help explain the contradiction.
Selection (C) is too vaguely worded to be of much help. Perhaps only two starting players failed to respond while all the other starting players responded to the survey. This might help explain the contradiction if a larger percentage of nonstarters failed to respond.
If Selection (D) were true, then it would not help resolve the contradiction. Rather, it would make the contradiction more inexplicable, particularly if we assume that the people who responded were correct in their responses.
Finally, Selection (E) might help explain the contradiction if good players who played later in the game were confused about whether they were classified as starters or not. But this answer is not the best answer. Selection (B) is by far the best answer
General Discussion
15 Mar 2021, 08:12
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We are looking for the most helpful explanation for the apparent discrepancy in the statistics.
The apparent discrepancy is the following:
Fact 1: Of the people who responded to the survey, 75% said they had started for their respective team.
Fact 2: However, the “actual number” of people who had started was 50% (of the actual players).
The “scope shift” in the basis upon which the statistics are based will most likely help to explain this discrepancy. Fact 1 is a percentage based on the people who “responded” to the survey. This number may very well be different than the total number of “actual” players on the team.
If most of the respondents were ppl who had started, then it would make sense that Fact 1 is skewed more towards “starters” than is the actual number.
(A) suggests that a very small number of survey participants were incorrect in their response to the survey. Depending on the size of the teams and amount of players involved, this may or may not be enough to account for the apparent discrepancy in the statistics. It does not seem to be strong enough to explain the significant difference.
(C) tells us that not all starting players responded to the survey. This fact, if true, would deepen the paradox. If there are some starters who didn’t even bother to respond to the survey, then how can it be that the percentage of starters, as registered by the survey, is larger than than the ACTUAL percentage of starters (based on all the players)? We would expect the survey percentage to be less than the actual percentage.
(D) also deepens the paradox. If almost all relevant people responded to the survey (and assuming they did so truthfully), then the percentage provided by the survey would seem to be based on a good representative sample of the entire population of players. We would expect the statistic in Fact 1 to be almost equivalent to the statistic in Fact 2.
(E): Wether or not good players were “held out” until later in the game does not help us understand why there exists a discrepancy in the statistics describing the percentage of players who had started.
However, if what (B) tells us were true - a disproportionately high number of starters responded to the survey - then this fact suggests that the statistic provided by the survey is based on a skewed sample of the population. If most of the respondents were starters, we would expect the percentage of respondents who said they had started to be greater than the percentage of actual players who had started.
Answer (B) helps the most in explaining the apparent paradox.
Posted from my mobile device
The apparent discrepancy is the following:
Fact 1: Of the people who responded to the survey, 75% said they had started for their respective team.
Fact 2: However, the “actual number” of people who had started was 50% (of the actual players).
The “scope shift” in the basis upon which the statistics are based will most likely help to explain this discrepancy. Fact 1 is a percentage based on the people who “responded” to the survey. This number may very well be different than the total number of “actual” players on the team.
If most of the respondents were ppl who had started, then it would make sense that Fact 1 is skewed more towards “starters” than is the actual number.
(A) suggests that a very small number of survey participants were incorrect in their response to the survey. Depending on the size of the teams and amount of players involved, this may or may not be enough to account for the apparent discrepancy in the statistics. It does not seem to be strong enough to explain the significant difference.
(C) tells us that not all starting players responded to the survey. This fact, if true, would deepen the paradox. If there are some starters who didn’t even bother to respond to the survey, then how can it be that the percentage of starters, as registered by the survey, is larger than than the ACTUAL percentage of starters (based on all the players)? We would expect the survey percentage to be less than the actual percentage.
(D) also deepens the paradox. If almost all relevant people responded to the survey (and assuming they did so truthfully), then the percentage provided by the survey would seem to be based on a good representative sample of the entire population of players. We would expect the statistic in Fact 1 to be almost equivalent to the statistic in Fact 2.
(E): Wether or not good players were “held out” until later in the game does not help us understand why there exists a discrepancy in the statistics describing the percentage of players who had started.
However, if what (B) tells us were true - a disproportionately high number of starters responded to the survey - then this fact suggests that the statistic provided by the survey is based on a skewed sample of the population. If most of the respondents were starters, we would expect the percentage of respondents who said they had started to be greater than the percentage of actual players who had started.
Answer (B) helps the most in explaining the apparent paradox.
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