A botanical researcher wishes to design a survey to estimate the number of birch trees in a study area. The study area has been divided into 1000 units or plots. From previous experience, the variance in the number of stems per plot is known to be approximately σ2 ≈ 45.
Using simple random sampling, what sample size should be used to estimate the total number of trees in the study area to within 500 trees of the true value with 95% confidence? To within 1000 trees? To within 2000 trees?