Student Amount spent Student Amount spent Student Amount spent 30 11 29 21 9 2 22 12 21 22 15 3 10 13 13 23 6 4 62 14 15 24 93 5 28 15 23 25 21 6 31 16 32 26 20 7 40 17 14 27 13 8 29 18 29 28 12 9 17 19 48 29 29 10 51 20 50 30 38 Table 1: Data for Problem 3 Problem 3 The design effect of Bernoulli sampling is defined as deff( BE) = V BE ( ty ) VERSWOR(ty) where VBE(ty) is given by (4.22) in the course notes and VSRSWOR(ty) is given by (4.4). Show that deff( BE) = N - N + CV (y) 2' where CV(y) = Sy/yu. The coefficient of variation of y is a "standardized" measure of its variability. This result shows that Bernoulli sampling is virtually always less efficient than simple random sampling without replacement. Why do you think this is the case? Hint: In the numerator, you may want to add and subtract yu