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Question 11 of 30

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M:C:MC:SET:1B

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SAT

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PSAT/NMSQT

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PSAT 10

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Problem Solving and Data Analysis

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Questions 10 and 11 refer to the following information.

A survey about voter participation in the 2012 US presidential election was conducted among a randomly chosen sample of US citizens. The table summarizes the results by age group.

Reported Voting by Age Group
Age group VotedDid not voteNo responseTotal
18–34 303 232 95 630
35–54 47117795743
55–74 43110168600
75 and older1243518177
Total1,3295452762,150

A second sample of 50 people from the 18–34 age group who reported voting in the 2012 presidential election were selected at random and asked which candidate they voted for. Of these people, 29 responded that they voted for Candidate A, and 21 responded that they voted for someone else. Based on this information, which of the following is the most appropriate estimate of the number of people from the 18–34 age group in the survey who voted for Candidate A in the 2012 presidential election?

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1,247

Correct Answer: 
No

771

Correct Answer: 
No

365

Correct Answer: 
No

176

Correct Answer: 
Yes

Choice D is the correct answer. This question asks students to extrapolate from a random sample to estimate the number of survey participants from the 18–34 age group who voted for Candidate A. This is done by multiplying the fraction of people in the random sample who voted for Candidate A by the total number of people in the survey in the 18–34 age group:  2950 × 303 ≈ 176 people.

Students without a clear grasp of this context and its representation in the table might arrive at one of the other answers listed.

Choice A is not the correct answer. The student may not have multiplied the fraction of the sample by the correct subgroup of people (people in the 18–34 age group in the survey who voted). This answer may result from multiplying the fraction of the sample who voted for Candidate A by the total number of people in the survey, 2,150, which is an incorrect application of the information.

Choice B is not the correct answer. The student may not have multiplied the fraction of the sample by the correct subgroup of people (people in the 18–34 age group in the survey who voted). This answer may result from multiplying the fraction of the sample who voted for Candidate A by the total number of people in the survey who voted, 1,329, which is an incorrect application of the information.

Choice C is not the correct answer. The student may not have multiplied the fraction of the sample by the correct subgroup of people (people in the 18–34 age group in the survey who voted). This answer may result from multiplying the fraction of the sample who voted for Candidate A by the total number of people in the 18–34 age group, 630, which is an incorrect application of the information.

Question Difficulty: 
medium
Objective: 

Students must extrapolate from a random sample to estimate a population parameter.