Consider a population of size N = 20 such that yd = a + bi, i = 1, . . . ,20, for some positive constants a and b. Such a population is said to have a linear trend. We consider systematic samples of size n = 4. (a) Show that the variance of t; under systematic sampling is equal to 800532. (b) Show that the variance of if; under simple random sampling Without replacement is equal to 2800132. Hint: Start with the expression fo the variance of it; under both sampling designs. Remark: This exercise sugests that, in the case of a linear trend, systematic sampling is more efficient than simple random sampling Without replacement