Why does the sample size play such an important role in reducing the standard error of the mean? What are the implications of increasing the sample size?

What will be an ideal response?

The standard error of the mean is the standard deviation of the population you are sampling from divided by the square root of the sample size. So, mathematically as the sample size increases, the standard error naturally decreases. But there is more to this, because the standard error is the standard deviation of the sample means. So, as the sample size increases, the sample means are deviating less and less from the true population mean. Hence, as we sample more, we get statistics which are closer to the true parameters and our inference methods will improve. This is true for sampling distributions of mean, proportions, and variances.