Which of the following correctly describes how to calculate the mean and standard deviation of the sampling distribution for sample means?

• A. The mean is equal to the sample mean, and the standard deviation is equal to the population standard deviation.
• B. The mean is equal to the population mean, and the standard deviation is equal to the population standard deviation divided by the square root of the sample size.
• C. The mean is equal to the sample mean, and the standard deviation is equal to the population standard deviation divided by the sample size.
• D. The mean is equal to the population mean, and the standard deviation is equal to the population standard deviation multiplied by the square root of the sample size.

Answer: (B)

Verified step by step guidance

1. Identify the concept of a sampling distribution of sample means, which is a distribution of means from multiple samples taken from the same population.
2. Understand that the mean of the sampling distribution of sample means is equal to the population mean. This is because the sample means are unbiased estimators of the population mean.
3. Recognize that the standard deviation of the sampling distribution of sample means is known as the standard error. It measures the variability of sample means around the population mean.
4. Calculate the standard error by dividing the population standard deviation by the square root of the sample size. This accounts for the fact that larger samples tend to have means closer to the population mean.
5. Conclude that the correct description is: The mean is equal to the population mean, and the standard deviation is equal to the population standard deviation divided by the square root of the sample size.