How is the standard error calculated?

The standard error is a statistical measure that quantifies the variability of a sample mean across different samples drawn from the same population. It is crucial in inferential statistics as it helps to understand how representative the sample mean is of the population mean.

The standard error is calculated by taking the standard deviation of the sample and dividing it by the square root of the sample size. This approach allows for the estimation of how much the sample mean is likely to vary from the true population mean. As the sample size increases, the square root of the sample size increases, leading to a smaller standard error. This indicates that larger samples provide more reliable estimates of the population mean because they tend to reduce the impact of sampling variability.

In contrast, the other options suggest calculations that do not align with the concept of standard error. Simply adding or multiplying the sample size by the standard deviation does not accurately reflect how sampling variability is assimilated into the measure of standard error. Similarly, squaring the sample size does not provide a meaningful statistic regarding the precision of the sample mean, as it does not involve the variability of the data itself. Hence, dividing the standard deviation by the square root of the sample size is the correct method to calculate the standard error.