A researcher has collected all possible samples of a size of

A researcher has collected all possible samples of a size of 150 from a population and listed the sample means for each of these samples. If the average of the sample means is 450.55, what would be the numerical value of the true population mean?

Solution

If a researcher literally took all possible sample means of a given size and took their average, it would be equal to population mean if each point was equally likely to be selected (so is the case in simple random sampling)

Thus true mean is 450.55