Which of the following is true of the sampling distribution

Which of the following is true of the sampling distribution of means? a) The sampling distribution of the means approximates the normal curve b) The mean of a sampling distribution of means is equal to the population mean c) The standard deviation of a sampling distribution of means is smaller than the standard deviation of the population d) all of the above

Solution

The central limit theorem states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough.

The mean of the sample means will be the mean of the population.

The standard deviation of the sample means (known as the standard error of the mean) will be smaller than the population mean and will be equal to the standard deviation of the population divided by the square root of the sample size.

Therefore, option d) is true.

i.e. all of the above.