If all possible random samples of size n are taken from a population, and the mean of each sample is determined, the mean of the sample distribution is: A. exactly the same as the population mean. B. larger than the population mean. C. smaller than the population mean. D. unrelated to the population mean.

Question

Beau Mendez

Mathematics

11 November, 08:57

If all possible random samples of size n are taken from a population, and the mean of each sample is determined, the mean of the sample distribution is: A. exactly the same as the population mean. B. larger than the population mean. C. smaller than the population mean. D. unrelated to the population mean.

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Gordon Avila · Answer 1

A. exactly the same as the population mean.

Step-by-step explanation: This demonstration illustrates Rule 1 of the Central Limit Theorem: The mean of the population and the mean of the sampling distribution of means will always have the same value. Thus, the sampling distribution of the mean will have a normal shape, even though the population distribution does not.

To calculate the mean, add up all the values and divide by the number of values. There are two types of arithmetic mean: population mean and the sample mean.