output: github_document: default html_document: default knit: (function(inputFile, encoding) { rmarkdown::render(inputFile, encoding = encoding, output_format = “all”) }) editor_options: markdown: wrap: 72 —
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.4.3library(dplyr)## Warning: package 'dplyr' was built under R version 4.4.3##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionPoblacion
# Definir los datos de los estratos manualmente
stratum <- c("A", "B", "C")
Nh <- c(3000, 4000, 5000) # Tamaños de población por estrato
Sh <- c(48, 79, 76) # Desviaciones estándar por estrato
# Combinar en un data frame para mejor manejo
strata_data <- data.frame(stratum, Nh, Sh)
strata_data## stratum Nh Sh
## 1 A 3000 48
## 2 B 4000 79
## 3 C 5000 76# Calcular proporciones
N <- sum(strata_data$Nh)
mutate(strata_data, porcentaje = Nh / N)## stratum Nh Sh porcentaje
## 1 A 3000 48 0.2500000
## 2 B 4000 79 0.3333333
## 3 C 5000 76 0.4166667strata_data## stratum Nh Sh
## 1 A 3000 48
## 2 B 4000 79
## 3 C 5000 76N_total<- sum(strata_data$Nh)
strata_data = strata_data %>% mutate(peso= Nh/N_total) %>% mutate(nh = round(400*peso,0))%>%
mutate(peso_optimo= Nh*Sh) %>%
mutate(nh_optimo = round(400*peso_optimo / sum(peso_optimo),0))
strata_data## stratum Nh Sh peso nh peso_optimo nh_optimo
## 1 A 3000 48 0.2500000 100 144000 69
## 2 B 4000 79 0.3333333 133 316000 150
## 3 C 5000 76 0.4166667 167 380000 181set.seed(123)
# Parámetros poblacionales
N_A <- 3000; mu_A <- 50; sigma_A <- 10; poblacion_A <- rnorm(N_A, mean = mu_A, sd = sigma_A)
N_B <- 4000; mu_B <- 65; sigma_B <- 25; poblacion_B <- rnorm(N_B, mean = mu_B, sd = sigma_B)
N_C <- 5000; mu_C <- 80; sigma_C <- 50; poblacion_C <- rnorm(N_C, mean = mu_C, sd = sigma_C)
N_total <- sum(N_A, N_B, N_C)
data <- data.frame(N_A, N_B, N_C, N_total)set.seed(456)
sample_A<- sample(poblacion_A, size = 100, replace = FALSE)
sample_A## [1] 69.39756 60.24475 63.38975 45.88079 52.88170 52.29395 37.80190 67.79038
## [9] 44.82018 52.46799 53.77388 49.72653 61.81618 48.31892 31.93107 53.00132
## [17] 41.48635 47.94174 40.03509 42.34001 45.31300 39.28253 67.51757 54.77037
## [25] 28.01077 71.61416 58.84650 49.77166 47.58209 37.77597 40.52525 58.82923
## [33] 40.95785 75.42904 54.26464 64.74314 50.07290 38.74603 33.32525 47.85495
## [41] 47.39168 49.99615 47.95237 47.89266 46.87456 49.02588 59.62528 72.81967
## [49] 29.06361 53.03529 39.06699 53.31434 54.27069 50.56017 61.95206 64.96822
## [57] 55.57012 61.68384 62.46424 54.54769 47.64300 65.32424 48.55951 58.70434
## [65] 50.37788 54.33676 36.83490 54.44400 51.19245 41.40985 43.13976 48.09641
## [73] 59.47231 42.00486 53.89331 60.51701 38.14520 63.70004 38.87455 27.43465
## [81] 61.48808 47.84619 32.48932 47.06387 55.04126 48.84778 50.87244 61.06837
## [89] 50.84737 68.66852 45.72804 31.65080 51.74136 61.45263 40.86434 44.06051
## [97] 39.36674 48.80547 54.83618 70.06681sample_B<- sample(poblacion_B, size = 133, replace = FALSE)
sample_B## [1] 40.636669 51.203138 98.110435 85.113863 73.908353 46.314495
## [7] 59.789372 55.819754 52.695227 93.938065 72.078312 76.919986
## [13] 61.209631 40.281340 57.553268 7.380116 24.428793 73.279458
## [19] 64.738855 83.151902 72.378675 99.339153 75.184227 39.830568
## [25] 33.149525 49.221159 79.579944 49.796287 51.501939 29.288135
## [31] 60.258378 79.055845 20.927318 75.232461 13.144835 69.638364
## [37] 32.486325 68.486778 33.770439 88.149317 76.601235 55.782891
## [43] 22.273496 35.421651 49.695706 82.837245 31.869218 79.812428
## [49] 39.405921 49.442447 80.219645 75.283767 94.261301 43.174137
## [55] 85.454055 88.840026 66.474387 81.490443 31.109523 60.068245
## [61] 65.830601 84.788294 78.116110 84.009579 146.897707 22.336759
## [67] 15.766300 61.997131 105.801466 50.417202 63.682461 25.377560
## [73] 23.997500 66.557205 34.421948 64.716834 97.782040 128.509216
## [79] 69.699119 52.205651 35.957578 73.868470 87.449606 85.646659
## [85] 53.814780 66.550660 77.174945 45.128586 55.327698 93.189837
## [91] 107.077102 83.030797 25.117712 46.308131 29.511541 63.125508
## [97] 68.405363 62.365290 48.206651 87.798599 66.461424 27.200385
## [103] 92.273784 106.784211 107.869030 71.265446 87.934059 111.445531
## [109] 47.258098 68.250456 61.222851 86.596199 83.662778 40.669651
## [115] 75.090518 102.585510 82.418135 10.650089 39.048949 82.567396
## [121] 21.800644 92.463329 88.390858 41.770089 80.534827 83.361455
## [127] 73.804022 114.627795 31.665852 75.565211 66.573443 116.346529
## [133] 68.998966sample_C<- sample(poblacion_C, size = 167, replace = FALSE)
sample_C## [1] 141.4659159 -50.0634313 92.6227893 125.5015525 191.2400409 11.1939377
## [7] 116.3011875 192.8632859 143.0668880 2.2784721 105.1950593 45.8309742
## [13] 93.5504010 61.4513177 2.6279853 124.8144948 42.8957926 -27.2356349
## [19] 116.2531126 81.5026593 67.5760314 125.9737181 187.9294395 38.7282810
## [25] 70.6557008 60.7678495 118.6717212 66.7393889 176.5191247 18.1951608
## [31] 161.3439530 41.3617676 2.1551984 170.3418196 123.4461575 58.5362551
## [37] -50.6413849 24.0684910 79.1351607 42.0826751 97.9545231 35.8195157
## [43] 59.1723719 114.5298701 110.3105530 -2.5165668 47.8961247 159.9611958
## [49] 18.9995972 86.0811321 84.9554250 98.5606874 111.4151635 108.2846437
## [55] 76.0129245 136.3928441 -32.2844578 31.9942533 55.8765083 80.1139382
## [61] 95.0331341 88.1650146 54.9023206 120.3755352 77.3044776 97.6496808
## [67] 103.1692791 138.9280982 32.2841939 -9.8119910 98.8473765 60.9459952
## [73] 31.2480205 95.7721545 99.4848807 115.4961315 75.2691903 100.6113554
## [79] -18.1015774 134.3833411 38.1352740 135.2800278 -25.8440781 92.6889727
## [85] 208.2129207 59.4341097 104.6215132 90.9390085 106.6992918 121.1875030
## [91] 68.3094219 150.7585593 79.4552235 17.2525635 43.0591628 53.0892844
## [97] 46.8516325 97.5001261 52.5882738 109.8736310 7.2937017 108.4966603
## [103] 104.4182366 102.7681073 23.1373706 103.3489046 85.3495338 85.2116583
## [109] 113.7754076 0.7981494 80.4229321 81.0994795 91.0602348 139.6734020
## [115] 41.3194251 54.0182279 140.4450870 44.9789668 33.9984888 151.7054440
## [121] 43.3786981 69.0340503 40.8256509 51.4547212 94.3308082 101.6786089
## [127] 94.4172136 138.7525045 74.3630785 -6.4110224 37.2763033 49.3504177
## [133] 103.8018660 30.0249973 30.5018438 108.3622121 59.3289078 58.1044815
## [139] 122.9075466 61.8241699 48.4489058 100.3590529 127.0215730 113.7123037
## [145] 202.8450536 46.4394010 65.6673877 45.8900271 115.6467308 40.7991866
## [151] 58.0314132 95.1014235 131.7257726 111.0204489 86.5715398 196.8522311
## [157] -22.1905209 48.9194496 63.8543184 109.7073299 83.3995642 68.8621260
## [163] 38.7735958 128.8010526 115.8179168 101.7378727 161.5281848mean(sample_A)## [1] 50.8156mean(sample_B)## [1] 64.764mean(sample_C)## [1] 80.00295media_poblacional <- (mean(poblacion_A) * N_A + mean(poblacion_B) * N_B + mean(poblacion_C) * N_C) / N_total
media_poblacional## [1] 67.56835# Calcular la media muestral estratificada estimada
n_A <- 100
n_B <- 133
n_C <- 167
n_total <- n_A + n_B + n_C# Media de cada muestra
media_A <- mean(sample_A)
media_B <- mean(sample_B)
media_C <- mean(sample_C)# Estimador de la media estratificada
media_estratificada <- (media_A * N_A + media_B * N_B + media_C * N_C) / N_total
media_estratificada## [1] 67.62646set.seed(456)
sample_A <- sample(poblacion_A, size = 69, replace = FALSE)
sample_B <- sample(poblacion_B, size = 150, replace = FALSE)
sample_C <- sample(poblacion_C, size = 181, replace = FALSE)media_A <- mean(sample_A)
media_B <- mean(sample_B)
media_C <- mean(sample_C)
media_A## [1] 51.47921media_B## [1] 64.78471media_C## [1] 80.99149media_poblacional <- (mean(poblacion_A) * N_A + mean(poblacion_B) * N_B + mean(poblacion_C) * N_C) / N_total
media_poblacional## [1] 67.56835n_A <- 69
n_B <- 150
n_C <- 181
n_total <- n_A + n_B + n_C
media_estratificada <- (media_A * N_A + media_B * N_B + media_C * N_C) / N_total
media_estratificada## [1] 68.21116error_absoluto <- abs(media_poblacional - media_estratificada)
error_absoluto## [1] 0.6428104