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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 was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results.

Reported Voting by Age (in thousands)
 VotedDid Not VoteNo ResponseTotal
18- to 34-year-olds30,32923,2119,46863,008
35- to 54-year-olds47,08517,7219,47674,282
55- to 74-year-olds43,07510,0926,83159,998
People 75 years old and over12,4593,5081,82717,794
Total132,94854,53227,602215,082

Of the 18- to 34-year-olds who reported voting, 500 people were selected at random to do a follow-up survey where they were asked which candidate they voted for. There were 287 people in this follow-up survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the follow-up survey and the initial survey, which of the following is most likely to be an accurate statement?

Select an Answer

About 123 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

Correct Answer: 
No

About 76 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

Correct Answer: 
No

About 36 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

Correct Answer: 
No

About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

Correct Answer: 
Yes

View Correct Answer

Choice D is the correct answer. This question asks students to extrapolate from a random sample to estimate the number of 18- to 34-year-olds 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 population of voting 18- to 34-year-olds: 287 over 500 cross times 30 comma 329 comma 000 almost equal to 17 space million comma choice D.

Students without a clear grasp of the context and its representation in the table might easily 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 (18- to 34-year-olds who voted). This answer may result from multiplying the fraction by the entire population, 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 (18- to 34-year-olds who voted). This answer may result from multiplying the fraction by the total number of people who voted, 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 (18- to 34-year-olds who voted). This answer may result from multiplying the fraction by the total number of 18- to 34-year-olds, which is an incorrect application of the information.

Question Difficulty: 
medium
Objective: 

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