An investigator is interested in estimating the total number of "count trees" (trees larger than a specified size) on a plantation of N = 1500 acres. This information is used to determine the total volume of lumber for trees on the plantation. A simple random sample of n = 100 one-acre plots was selected, and each plot was examined for the number of count trees. The sample average for the n = 100 one-acre plots was ȳ = 25.2 with a sample variance of s² = 136.
(a) Estimate the total number of count trees on the plantation. Place a bound on the error of estimation.
(b) Using the results of the survey described above, determine the sample size required to estimate τ, the total number of trees on the plantation, with a bound on the error of estimation ε = 1500.