Example 3.3 Lohr, page 81

discipline <- c("Literature", "Classics", "Philosophy", "History", "Linguistics", "Political Science", "Sociology")
N_h <- c(9100, 1950, 5500, 10850, 2100, 5500, 9000)  #membership
phat_h <- c(0.38, 0.27, 0.18, 0.19, 0.36, 0.13, 0.26)  #FemaleMembers(%)

sumof_N_h <- sum(N_h)
sumof_N_h
## [1] 44000
N_h_over_N_phat_h <- N_h/(sum(N_h)) * phat_h
N_h_over_N_phat_h
## [1] 0.07859091 0.01196591 0.02250000 0.04685227 0.01718182 0.01625000
## [7] 0.05318182
phat_strata <- sum(N_h_over_N_phat_h)
phat_strata
## [1] 0.2465227
n_h <- c(636, 451, 481, 611, 493, 575, 588)  #ValidReturns

Var_phat_strata <- sum((1 - n_h/N_h) * (N_h/sum(N_h))^2
                       * (phat_strata * (1 - phat_strata)/(n_h - 1)))
Var_phat_strata
## [1] 5.281232e-05
sd_phat_strata <- sqrt(Var_phat_strata)
sd_phat_strata
## [1] 0.007267209
# c(915,633,658,855,667,833,824) #NumberMailed

# 95% C.I. for phat
C_I_LL <- phat_strata - 1.96 * sd_phat_strata
C_I_LL
## [1] 0.232279
C_I_UL <- phat_strata + 1.96 * sd_phat_strata
C_I_UL
## [1] 0.2607665
Total_LL <- sumof_N_h * C_I_LL
Total_LL
## [1] 10220.28
Total_UL <- sumof_N_h * C_I_UL
Total_UL
## [1] 11473.72
sessionInfo()
## R version 3.4.2 (2017-09-28)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Linux Mint 18.2
## 
## Matrix products: default
## BLAS: /usr/lib/libblas/libblas.so.3.6.0
## LAPACK: /usr/lib/lapack/liblapack.so.3.6.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## loaded via a namespace (and not attached):
##  [1] compiler_3.4.2  backports_1.1.2 magrittr_1.5    rprojroot_1.3-2
##  [5] tools_3.4.2     htmltools_0.3.6 yaml_2.1.16     Rcpp_0.12.15   
##  [9] stringi_1.1.6   rmarkdown_1.8   knitr_1.18      stringr_1.2.0  
## [13] digest_0.6.14   evaluate_0.10.1