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Inference from sample statistics and margin of error SAT question
Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.
A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?
ExplanationShow
Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5 miles, it follows that between 
miles and 
miles, or between 4 and 5 miles, is plausibly the mean distance hiked for all visitors.
Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles hiked for all visitors to the park.
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