Question #c7e73ece - SAT Suite Question Bank

ID: c7e73ece

Modded SAT Question Bank by Abdullah Mallik

Views on Nuclear Energy Use
Response	Frequency
Strongly favor	56
Somewhat favor	214
Somewhat oppose	104
Strongly oppose	37

A researcher interviewed 411 randomly selected US residents and asked about their views on the use of nuclear energy. The table above summarizes the responses of the interviewees. If the population of the United States was 300 million when the survey was given, based on the sample data for the 411 US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it? (Round your answer to the nearest whole number.)

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Correct Answer:

Rationale

The correct answer is 94. Of those interviewed, $56 plus 214, equals 270$ “strongly favor” or “somewhat favor” the use of nuclear energy, and $104 plus 37, equals 141$ interviewees “somewhat oppose” or “strongly oppose” the use of nuclear energy. The difference between the sizes of the two surveyed groups is $270 minus 141, equals 129$ . The proportion of this difference among the entire group of interviewees is $the fraction 129 over 411$ . Because the sample of interviewees was selected at random from US residents, it is reasonable to assume that the proportion of this difference is the same among all US residents as in the sample. Therefore, the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it is $the fraction 129 over 411, end fraction, times 300$ , which to the nearest million is 94.

Question Difficulty: Hard