Consider the hypothetical population below, with population values:

a. Find the values of the population quantities tx, ty, Sx, Sy, R, and B.
b. Construct a table like that in Table 4.2, giving the sampling distribution of Nand ofˆtyr , for a sample of size n = 3.
c. Draw a histogram of the sampling distribution of ṫyr . Compare this histogram to a histogram of the sampling distribution of N.
d. Find the mean and variance of the sampling distribution of ṫyr . How do these compare to the mean and variance of N? What is the bias ofˆtyr?
e. Use Equation (4.6), together with the population quantities you calculated in (a) to find an approximation to Bias (ṫyr) = NBias (r ). How close is the approximation to the true bias in (c)?

y 0 7 3 7 81574 3 7 1 2 4 3135 Nu 12345678 9