Jackson et al. (1987) compared the precision of systematic and stratified sampling for estimating the average concentration of lead and copper in the soil. The 1-km2 area was divided into 100-m squares, and a soil sample was collected at each of the resulting 121 grid intersections. Summary statistics from this systematic sample are given below.

The investigators also post stratified the same region. Stratum A consisted of farmland away from roads, villages, and woodlands. Stratum B contained areas within 50m of roads, and was expected to have larger concentrations of lead. Stratum C contained
The woodlands, which were also expected to have larger concentrations of lead because the foliage would capture airborne particles. The data on concentration of lead and copper were not used in determining the strata. The data from the grid points falling in each stratum are in the following table:

a. Calculate a 95% CI for the average concentration of lead in the area, using the systematic sample. (You may assume that this sample behaves like an SRS.)
Repeat for the average concentration of copper.
b. Now use the post stratified sample, and find 95% CIs for the average concentration of lead and copper. How do these compare with the CIs in (a)? Do you think that using stratification in future surveys would increase precision?

Average Range Standard Deviation Element Lead Copper (mg kg) (mg kg1) (mg kg) 121 121 127 35 22-942 15-90 146 16 Average (mg kg) Range Standard Deviation (mg kg1) 28 232 Element Stratunm (mg kg) 71 259 189 28 50 45 22-201 36-942 88-308 15-68 22-90 31-69 Copper Copper Copper 18 8