Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for

Question

Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5 , with an associated margin of error of 1 . Which of the following is the most appropriate conclusion?

Accepted Answer

Choice A is correct. It's given that based on a random sample from a population, the estimated mean value for a certain variable for the population is 20.5 , with an associated margin of error of 1 . This means that it is plausible that the actual mean value of the variable for the population is between 20.5 - 1 and 20.5 + 1 . Therefore, the most appropriate conclusion is that it is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5 . Choice B is incorrect. The estimated mean value and associated margin of error describe only plausible values, not all the possible values, for the actual mean value of the variable, so this is not an appropriate conclusion. Choice C is incorrect. The estimated mean value and associated margin of error describe only plausible values for the actual mean value of the variable, not all the possible values of the variable, so this is not an appropriate conclusion. Choice D is incorrect. Since 20.5 is the estimated mean value of the variable based on a random sample, the actual mean value of the variable may not be exactly 20.5 . Therefore, this is not an appropriate conclusion.

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