Which of the following formulas correctly calculates the standard error of the mean for a data set with sample standard deviation $s$ and sample size $n$?

• A. $\frac{s}{n}$
• B. $\frac{s}{n+1}$
• C. $\frac{n}{s}$
• D. $\frac{s}{\sqrt{n}}$

Answer: (D)

Verified step by step guidance

1. Recall that the standard error of the mean (SEM) measures how much the sample mean is expected to vary from the true population mean. It is derived from the sample standard deviation and the sample size.
2. Identify the sample standard deviation as \(s\) and the sample size as \(n\) in the problem.
3. Understand that the SEM is calculated by dividing the sample standard deviation by the square root of the sample size, which accounts for the fact that larger samples tend to give more precise estimates of the population mean.
4. Write the formula for the standard error of the mean as: \[\text{SEM} = \frac{s}{\sqrt{n}}\]
5. Compare this formula to the options given and recognize that the correct formula matches the one where \(s\) is divided by the square root of \(n\), not simply \(n\) or \(n+1\).