Carry out the following “experiment” to test the validity of the sampling constant equation
mR2 = Ks
where m is the sample’s mass, R is the relative standard deviation for sampling, and Ks is the sampling constant.
Obtain a package of M&M’s, or other candy that comes in several colors. Select five M&M’s at random, recording the percentage that are brown (note: for this sample, m = 5). Return the M&M’s to the bag and repeat for a total of 7 trials. Continue in this manner using samples of 10, 15, 20, and 25 M&M’s. To analyze your data, do the following:
(a) Gather your data together in a table with column headings of “sample size”, “% Brown”, “average % Brown”, “standard deviation”, “R”, and “Ks”. Note that second and third columns will each have seven entries for each sample size, whereas the remaining columns will have but one entry per sample size.
(b) Examine your results for Ks and comment on the validity of the sampling constant equation for this population of M&M’s.
(c) Prepare a graph showing the average % Brown per trial on the y-axis and the sample size on the x-axis (a total of 35 data points). Using your average value for Ks, calculate the expected standard deviation for sample sizes of 1 – 10 and add points to your graph of ± 1 standard deviation about the global mean value (the average % Brown for all 35 trials). Connect these points with two smooth lines (one for +1 standard deviation and one for –1 standard deviation) and comment, again, on the validity of the sampling constant equation for this population of M&M’s.
