Problem Solving

Question

The formula for the standard error (standard deviation of the distribution of sample means) implies that as the sample size (n) increases, the size of the standard error decreases. Explain the role of the standard error in comparing the sample mean and the population mean. Use the definitions and concepts on sample means distribution and standard error and show examples comparing the sample mean and the population mean of a distribution when the standard error changes in value. 

Answer 1

The standard deviation is a measure of the variation in the data points. The stand error is a measure of the variation in the sample mean, which is an estimate of the population mean. So, the smaller the variation in the estimate of the population mean (i.e. standard error), the closer your estimate is to the real population mean. I'll leave it to you to create the necessary examples.

I suggest using a relatively small sample size for ease of the calculations.