Given the same total sample size (n = 1000), compute the optimal sample sizes (see Lecture 6) and enter these below. Assume that the true variance is S21 = 1459264, S22 = 193600, S23 = 15876, and S24 = 1849 in stratum 1, 2, 3, and 4, respectively. The relative stratum sizes are given in the Excel file (N1/N = 12.4, N2/N = 6.1, N3/N = 14.2, N4/N = 67.3). Hint: It is easiest to do the computations in four steps: • compute the Sh = sqrt(S2h), for all strata h=1,2,3,4 • compute Nh x Sh for all strata h=1,2,3,4 (you can use the percentages). Note: you can just use the relative stratum sizes (Nh/N, instead of Nh). This will give you the same answer as using the absolute stratum sizes Nh. • compute w = n / (N1 × S1 + N2 × S2 + N3 × S3 + N4 × S4). • then compute the optimal sample sizes as : w x Nh x Sh. You can use a calculator, or write the formulas in cells C14-G17 in the Excel file.