Question

what is the mean of the sample means?
the mean of the sample means is equal to the population mean, divided by the
population standard deviation.
the mean of the sample means is equal to the population mean.
the mean of the sample means is undefined because all possible sample means
can never be found.
the mean of the sample means is equal to the population mean,divided by the
sample size.
the mean of the sample means is equal to the population mean, divided by the
square root of the sample size.

Explanation:

Step1: Recall the Central Limit Theorem

The Central Limit Theorem states that for a population with mean \(\mu\) and standard deviation \(\sigma\), if we take random samples of size \(n\) from this population, the sampling distribution of the sample mean \(\bar{X}\) has mean \(E(\bar{X})=\mu\). This means that the average of all possible sample means (the mean of the sample means) is equal to the population mean. So, regardless of the sample size \(n\) (as long as the sampling is random and other basic assumptions are met), the mean of the sample means is equal to the population mean.

Answer:

The mean of the sample means is equal to the population mean.