Doubling the size of a sample will have what effect on the standard error of the mean?

Doubling the size of a sample leads to a reduction in the standard error of the mean. The standard error measures the variability of the sample mean estimate as it relates to the true population mean. Mathematically, the standard error is calculated as the standard deviation of the sample divided by the square root of the sample size.

As the sample size increases, the denominator of this formula (the square root of the sample size) increases, which results in a smaller standard error. Specifically, when the sample size is doubled, the square root of the sample size increases, effectively reducing the overall value of the standard error. This means that with a larger sample, we can expect our sample mean to be a more accurate reflection of the population mean, demonstrating less variability.

The relationship between sample size and standard error highlights the importance of larger samples in statistical analyses, as they provide more reliable estimates of population parameters.