Determine the sample mean and sample standard deviation of the sampling distribution of the mean.

Question

Determine the sample mean and sample standard deviation of the sampling distribution of the mean.

Answer 1

In order to determine the sample mean and sample standard deviation of the sampling distribution of the mean, we need to know the population mean and population standard deviation. This is because the sample mean and sample standard deviation of the sampling distribution are based on the population parameters.

The sample mean (denoted by "𝑥̅") of the sampling distribution of the mean is equal to the population mean (denoted by "𝜇"). The sample standard deviation (denoted by "𝑠̅") of the sampling distribution of the mean is equal to the population standard deviation (denoted by "𝜎") divided by the square root of the sample size (denoted by "𝑛").

Therefore, the sample mean of the sampling distribution of the mean is 𝜇, and the sample standard deviation of the sampling distribution of the mean is 𝜎/√𝑛.