Here are the commands we used in exploring bounds on the error of estimation in confidence intervals for a mean collected from a simple random sample in Minitab. To look at the sample size needed over a wide range of choices of B and sigma, we need to create a grid of values for B and sigma. For the bear data, we decided to look at all possible combinations of (B,sigma) where B ranged from 20 to 70 in increments of 10 and sigma ranged from 100 to 200 in increments of 20. To create this grid, we type: SET C1 6(20:70/10) SET C2 (100:200/20)6 C1 contains the sequence 20 30 40 50 60 70 repeated 6 times; C2 contains the sequence 100 120 140 160 180 200 where each term is repeated 6 times before the next term occurs. Note that you don't have to use an nxn grid; it just happened to be convenient in this case. Both columns now have 36 observations. We also need to store the population size as a constant; to do this, enter LET K1=5000 We can now evaluate the sample size needed to achieve the margin of error listed in C1 for the variance listed in C2: LET C3=K1*C2*C2/(((K1-1)*C1*C1/4.)+C2*C2) If we do a default contour plot now, it's unsuccessful since the sample size ranges over a couple orders of magnitude--it's probably best to do a wire mesh plot first. To do this, select 3D Wireframe Plot from Graph, enter c3 as Z then c2 for Y and c1 for X (the order of these last two doesn't matter). Hit OK and note that the resulting plot has a surface that's generally below 100 except for small B and large sigma. We can adjust the default contour plot by selecting Contour Plot from Graph, entering c3 for Z, c2 for Y and c1 for X then selecting Options..., clicking Values under Contour Levels and then entering 10:120/10 in the Values dialog box (you could also enter a column that had these values stored in it). Notice that the contour graph is now much more useful than the default contour graph with contours covering most of the surface of the grid. Moral: you need to do some fiddling around to get a useful graph.