Question

Using the trees data (in R) with volume as the variable of interest (y = trees$Volume) use simulation to compare random sampling without replacement (SRS) with the design random sampling with replacement for estimating the population mean. Use sample size n = 12 for each strategy. Estimate the population mean with the sample mean (nominal sample mean in the with-replacement case). To compare the strategies, use histograms, qqplots, calculations of mean of estimators, and mean square errors of estimators. Write a one-sentence conclusion（"The strategy ______ is recommended because _________." ）

Answer 1

Here strategy 2 is recommended i.e. sampling without replacement(WOR) beacuse the sample variance of strategy 1 i.e of sampling with replacement(WR) case is more than that of strategy 2 i.e WOR case.

The steps to do the above are as follows:-

a) data=trees$Volume

b)x=sample(data,12,replace = T)

c)y=sample(data,12,replace = F)

d) x
[1] 10.3 31.7 51.0 19.1 36.3 42.6 77.0 38.3 24.9 19.9 21.0 21.3

e) y
[1] 36.3 22.2 19.1 18.2 51.0 27.4 18.8 51.5 10.2 10.3 55.7 10.3

f) mean(x)
[1] 32.78333

g)mean(y)
[1] 27.58333

h)var(x)
[1] 328.9888
i)var(y)
[1] 286.6052

j)hist(x,xlab = "volume",main = "WR case")
k)hist(y,xlab = "volume",main = "WOR case")