Final answer:
The standard error of the mean is mathematically related to the population standard deviation (σ) and inversely proportional to the square root of the sample size (n), according to the central limit theorem.
Step-by-step explanation:
According to the central limit theorem, the standard error of the mean is mathematically related to sigma. This means that the standard error of the mean (SEM) is calculated as the population standard deviation (σ) divided by the square root of the sample size (n). So as your sample size increases, your SEM will decrease.
The central limit theorem also tells us that if we take sufficiently large samples from a population, the sampling distribution of the sample means will approach a normal distribution. This stands regardless of the shape of the original population distribution. The mean of this sampling distribution will equal the population mean, while the standard deviation equals the population standard deviation divided by the square root of the sample size (√n).