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 Ny¯ and of ˆtyr, for a sample of size n = 3.
c Draw a histogram of the sampling distribution of ˆtyr. Compare this histogram to a histogram of the sampling distribution of Ny¯.
d Find the mean and variance of the sampling distribution of ˆtyr. How do these compare to the mean and variance of Ny¯? What is the bias of ˆtyr?
e Use Equation (4.6), together with the population quantities you calculated in (a) to find an approximation to Bias (ˆtyr) = NBias (ˆ y¯r). How close is the approximation to the true bias in (c)?
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