Please show your codes and output in R. Please ignore Question (b) for systematic sampling.For Questions (c) and (d), please draw random samples in the two ways stated there, i.e., with either rows or columns (as you consider appropriate) as strata for (c) and as clusters for (d), and compare your answers.You should use R to draw the samples and then compute the estimates (by either hands or R) using the tree grid in the textbook.

Think of the accompanying grid of 0s and is as a rough aerial map of a planted forest in which the is represent diseased trees. You can see something of the pattern of the trees, but assume that you cannot count them accurately from the air. You need to conduct a ground survey to estimate the proportion of diseased trees. From the 150 trees in the forestyou are to sample 30 trees from which to construct your estimate. Design and carry out a sample survey and complete the analysis (estimate the proportion and calculate a margin of error) for each of the following designs: a. Simple random sample b. Systematic sample c. Stratified random sample with either rows or columns as strata, explaining your choice d. Cluster sample with either rows or columns as clusters, explaining your choice Compare your results with those of other students, and discuss which sampling design you think is best. TREE GRID Row CI C5 0 -- 0 0 0 ------- 0