Suppose that we conduct an experiment in which samples of size n are generated from a normal distribution having a known standard deviation σ. If we compute the range of each sample, we can estimate the distribution of the statistic R/σ. The expected value of this statistic is a factor that statisticians have labeled as d2 . If we know this value and a sample range, then we can estimate σ by R/d2. The values of d2 are shown below for sample sizes from 2 through 5.
nd2
2 …………………………1.128
3 …………………………1.693
4 …………………………2.059
5 …………………………2.326
Develop a sampling experiment on a spreadsheet to estimate these values of d2 by generating 1,000 samples of n random variates from a normal distribution with a mean of 0 and standard deviation of 3 (using the Excel function NORMINV). For each of the 1,000 samples, compute the range, and the value of R/σ. Use the average value of R/σ to estimate d2 for sample sizes n = 2 through 5. Compare your results to published factors shown above. How well did your experiment perform?