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Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Easy

In a study, the data from a random sample of a population had a mean of 37, with an associated margin of error of 3. Which of the following is the most appropriate conclusion that can be made about the population mean?

It is less than 37.

It is greater than 37.

It is between 34 and 40.

It is less than 34 or greater than 40.

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Explanation

Choice C is correct. It’s given that the mean of the data from a random sample of a population is 37, with an associated margin of error of 3. The most appropriate conclusion that can be made is that the mean of the entire population will fall between 37, plus or minus 3. Therefore, the population mean is between $37 minus 3, which equals 34$ and $37 plus 3, which equals 40$ .

Choice A is incorrect. While it’s an appropriate conclusion that the population mean is as low as $37 minus 3$ , or 34, it isn’t appropriate to conclude that the population mean is less than 34. Choice B is incorrect. While it’s an appropriate conclusion that the population mean is as high as $37 plus 3$ , or 40, it isn’t appropriate to conclude that the population mean is greater than 40. Choice D is incorrect. It isn’t an appropriate conclusion that the population mean is less than 34 or greater than 40.