Why are the standard error and the sampling distribution of the mean important?
Important statistical properties. Conclusions about the performance of a test or method are often based on the calculation of means and the assumed normality of the sampling distribution of means. If enough experiments could be performed and the means of all possible samples could be calculated and plotted in a frequency polygon, the graph would show a normal distribution. However, in most applications, the sampling distribution can not be physically generated (too much work, time, effort, cost), so instead it is derived theoretically. Fortunately, the derived theoretical distribution will have important common properties associated with the sampling distribution. • The mean of the sampling distribution is always the same as the mean of the population from which the samples were drawn. • The standard error of the mean can be estimated by the square root of SS over N or s over the square root of N or even SD/(N)1/2. Therefore, the sampling distribution can be calculated when the SD is w
