CHAPTER 5. CLUSTER SAMPLING WITH EQUAL PROBABILITIES
114 M 1 2 3 4 5 1 2 3 4 6 1 2 3 4 5
R2a 0.1 0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 0.5 0.8 0.8 0.8 0.8 0.8
sample size 310 171 124 101 87 310 233 207 194 181 310 279 269 264 260
5.14 (a) Treating the proportions as means, and letting Mi and mi be the number of female students in the school and interviewed, respectively, we have the following summaries. School M i mi smokers 1 792 25 10 2 447 15 3 3 511 20 6 4 800 40 27 Sum 2550 100 Var
ȳi 0.4 0.2 0.3 0.675
s2i .010 .011 .011 .006
t̂i 316.8 89.4 153.3 540.0 1099.5
t̂i − M i ŷ¯r -24.7 -103.3 -67.0 195.1
2 2
mi Mi i (1 − M ) mi i 243 147 139 86 614 s
17943
Then, 1099.5 = 0.43 2550 s 1 4 17943 1 SE [ŷ¯r ] = 1− + (614) 637.5 29 4 4(29) 1 √ = 3867.0 + 5.3 637.5 = 0.098. ŷ¯r =
(b) We construct a sample ANOVA table from the summary information in part (a). Note that 4
ssw =
4
mi
(yij − ȳi ) = (mi − 1)s2 , i
i=1 j=1
and
2
i=1
