Question: Israel's kibbutzim are by now well diversified beyond their agrarian roots, producing everything from lollipops to plastic pipe. These 282 widely scattered communes of several hundred members maintain hundreds of factories and other production facilities. An economist wants to estimate the average annual revenues of all kibbutz production facilities. Since each kibbutz has several production units, and since travel and other costs are high, the economist wants to consider a sample of 15 randomly chosen kibbutzim and find the annual revenues of all production units in the selected kibbutzim. From these data, the economist hopes to estimate the average annual revenue per production unit in all 282 kibbutzim. The sample results are as follows:
From these data, compute the cluster sampling estimate of the mean annual revenue of all kibbutzim production units, and give a 95% confidence interval for the mean.