# solution

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 NyÂ¯ and of Ë†tyr, for a sample of size n = 3.

c Draw a histogram of the sampling distribution of Ë†tyr. Compare this histogram to a histogram of the sampling distribution of NyÂ¯.

d Find the mean and variance of the sampling distribution of Ë†tyr. How do these compare to the mean and variance of NyÂ¯? What is the bias of Ë†tyr?

e Use Equation (4.6), together with the population quantities you calculated in (a) to find an approximation to Bias (Ë†tyr) = NBias (Ë† yÂ¯r). How close is the approximation to the true bias in (c)?

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