## **Core Concept**
The question tests understanding of statistical concepts in research methodology, specifically the variability of sample means from the population mean. This variation is quantified by the **standard error of the mean (SEM)**, which is a measure of how much the sample mean may vary from the population mean.

## **Why the Correct Answer is Right**
The correct formula for the standard error of the mean (SEM) is (SEM = frac{sigma}{sqrt{n}}), where (sigma) is the population standard deviation and (n) is the sample size. This formula shows that the variability of the sample mean from the population mean decreases as the sample size increases. This makes intuitive sense because larger samples are more representative of the population.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option does not represent any standard formula related to the variation of sample means from the population mean.
- **Option B:** Similarly, this option does not correspond to a recognized statistical measure for assessing the variability of sample means.
- **Option D:** This option also does not match any commonly used formula in statistics for describing the variation of sample means from the population mean.

## **Clinical Pearl / High-Yield Fact**
A crucial point to remember is that to decrease the standard error of the mean (and thus have a sample mean that is more likely to be close to the population mean), you should **increase the sample size**. This is because (SEM = frac{sigma}{sqrt{n}}), and as (n) increases, (SEM) decreases.

## **Correct Answer:** C.