In a medical study, a simple random sample of size 50 is obtained from a general population. Each sampled person's age is recorded, and his/her bone density (in appropriate units) is measured. The scatterplot shows the sample data.



You would like to estimate the average bone density in this population. From census data you know that the mean age in the population is 48. The mean age in your sample happens to be higher than this. You are considering three methods to estimate your target: "vanilla" (VN) estimation, ratio (RT) estimation, and regression (RG) estimation.

(a) Based on the information provided, which of the following is the order of your three estimates of population average bone density, from smallest to largest.

A. RT< VN < RG
B. RT < RG < VN
C. VN < RT < RG
D. VN < RG < RT
E. RG < VN < RT
F. RG < RT < VN
G. Insufficient information is provided to know for sure.


(b) Of the three methods, which one is clearly inappropriate for these data?

A. Ratio
B. Vanilla
C. Regression