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CHAPTER 5. CLUSTER SAMPLING WITH EQUAL PROBABILITIES
## Fixed effects: reading ~ 1 ## Value Std.Error DF t-value p-value ## (Intercept) 31.565 1.485056 190 21.25509 0 ## Standardized Within-Group Residuals: ## Min Q1 Med Q3 ## -2.5151010 -0.6911411 0.1162636 0.8693088
Max 1.6368259
## Number of Observations: 200 ## Number of Groups: 10 # extract the variance components VarCorr(readmixed) ## factor(schoolid) = pdLogChol(1) ## Variance StdDev ## (Intercept) 19.12775 4.373528 ## Residual 58.52342 7.650060 (a) The mean reading score is 30.604. The with-replacement SE is 1.5533. (b) The without-replacement SE is 1.4612, just a little bit smaller. 5.19 From the output in the previous exercise, the estimated proportion is 0.47829 with SE 0.0657 and 95% CI [0.330, 0.627]. The CI is quite wide! 5.20 From the R code for Exercise 5.18, we have µ̂ = 31.565 with SE 1.485. Here is analogous code for the MIXED procedure in SAS software: proc mixed data=schools; class schoolid; model reading = / solution cl; random schoolid; run;
5.21 With the different costs, the last two columns of Table 5.8 change. The table now becomes: Number of Stems Sampled per Site 1 2 3 4 5
ŷ¯ 1.12 1.01 0.96 0.91 0.91
SE(ŷ¯) 0.15 0.10 0.08 0.07 0.06
Cost to Sample One Field 50 70 90 110 130
Relative Net Precision 0.15 0.14 0.13 0.12 0.12
