It is plausible that the actual mean value of the variable for the population is between and .
It is not possible that the mean value of the variable for the population is less than or greater than .
Every value of the variable in the population is between and .
The mean value of the variable for the population is .
Explanation
Correct answer: A.
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 , with an associated margin of error of . This means that it is plausible that the actual mean value of the variable for the population is between and . Therefore, the most appropriate conclusion is that it is plausible that the actual mean value of the variable for the population is between and .
Desmos solution:
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Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice B
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
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
Choice D is incorrect. Since is the estimated mean value of the variable based on a random sample, the actual mean value of the variable may not be exactly . Therefore, this is not an appropriate conclusion.