4. Suppose that we conduct an experiment in which samples of size n are generated from a normal distribution having a known standard deviation s . If we compute the range of each sample, we can estimate the distribution of the statistic R / s . The expected value of this statistic is a factor that statisticians have labeled as d 2 .

If we know this value and a sample range, then we can estimate s by R / d 2 . The values of d 2 are shown below for sample sizes from 2 through 5.

n d2 2 1.128 3 1.693 4 2.059 5 2.326 Develop a sampling experiment on a spreadsheet to estimate these values of d 2 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 / s . Use the average value of R / s to estimate d 2 for sample sizes n = 2 through 5. Compare your results to published factors shown above. How well did your experiment perform?