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Inference from sample statistics and margin of error SAT question
Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.
| 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.)
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
The correct answer is 94. Of those interviewed, 
“strongly favor” or “somewhat favor” the use of nuclear energy, and 
interviewees “somewhat oppose” or “strongly oppose” the use of nuclear energy. The difference between the sizes of the two surveyed groups is 
. The proportion of this difference among the entire group of interviewees is 
. 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 
, which to the nearest million is 94.
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