Using Excel to generate empirical sampling distributions

Abstract

Teachers in many introductory statistics courses demonstrate the Central Limit Theorem by using a computer to draw a large number of random samples of size n from a population distribution and plot the resulting empirical sampling distribution of the sample mean. There aremany computer applications that can be used for this (see, for example, the Rice Virtual Lab in Statistics: http://www.ruf.rice.edu/~lane/rvls.html). The effectiveness of such demonstrations has been questioned (see delMas et al (1999))) but in the work presented in this paper we do not rely on sampling distributions to convey or teach statistical concepts; only that the sampling distribution is independent of the distribution of the population, provided the sample size is sufficiently large.We describe a lesson that starts out with a demonstration of the CTL, but sample from a (finite) population where actual census data is provided; doing this may help students more easily relate to the concepts &ndash; they can see the original data as a column of numbers and if the samples are shown they can also see random samples being taken. We continue with this theme of sampling from census data to teach the basic ideas of inference. We end up with standard resampling/bootstrap procedures.We also demonstrate how Excel can provide a tool for developing a learning objects to support the program; a workbook called Sampling.xls is available from www.deakin.edu.au/~rodneyc/PS &gt; Sampling.xls.<br /