Mónica Isabel Blanco 2025-11-13
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## lat long depth mag
## Min. :-38.59 Min. :165.7 Min. : 40.0 Min. :4.00
## 1st Qu.:-23.47 1st Qu.:179.6 1st Qu.: 99.0 1st Qu.:4.30
## Median :-20.30 Median :181.4 Median :247.0 Median :4.60
## Mean :-20.64 Mean :179.5 Mean :311.4 Mean :4.62
## 3rd Qu.:-17.64 3rd Qu.:183.2 3rd Qu.:543.0 3rd Qu.:4.90
## Max. :-10.72 Max. :188.1 Max. :680.0 Max. :6.40
## stations
## Min. : 10.00
## 1st Qu.: 18.00
## Median : 27.00
## Mean : 33.42
## 3rd Qu.: 42.00
## Max. :132.00poblacion <- quakes
N_poblacion <- nrow(poblacion)
media_poblacional <- mean(poblacion$mag)
desviacion_poblacional <- sd(poblacion$mag)
cat("Tamaño de la Población (N):", N_poblacion, "\n")## Tamaño de la Población (N): 1000## Media Poblacional de Magnitud (mu): 4.62## Desviación Estándar Poblacional (sigma): 0.403#Muestra
set.seed(123)
n_muestra <- 150
muestra <- sample_n(poblacion, size = n_muestra, replace = FALSE)
muestra## lat long depth mag stations
## 1 -21.50 185.20 139 4.4 15
## 2 -18.08 180.70 628 5.2 72
## 3 -17.84 181.48 542 4.1 20
## 4 -21.31 180.84 586 4.5 17
## 5 -32.20 179.61 422 4.6 41
## 6 -22.41 183.99 128 5.2 72
## 7 -16.21 186.52 111 4.8 30
## 8 -13.47 172.29 64 4.7 14
## 9 -30.64 181.20 175 4.0 16
## 10 -23.73 182.53 232 5.0 55
## 11 -18.20 183.68 107 4.8 52
## 12 -21.00 181.66 600 4.4 10
## 13 -19.77 181.40 630 5.1 54
## 14 -18.44 181.04 624 4.2 21
## 15 -28.10 182.25 68 4.6 18
## 16 -21.24 180.81 605 4.6 34
## 17 -19.85 184.51 184 4.4 26
## 18 -21.56 183.23 271 4.4 36
## 19 -15.48 167.53 128 5.1 61
## 20 -18.68 184.50 174 4.5 34
## 21 -27.38 182.39 69 4.5 12
## 22 -37.03 177.52 153 5.6 87
## 23 -27.27 182.36 65 4.7 21
## 24 -18.97 169.44 242 5.0 41
## 25 -17.94 181.49 537 4.0 15
## 26 -19.50 186.90 58 4.4 20
## 27 -33.00 182.40 176 4.6 28
## 28 -18.83 182.26 575 4.3 11
## 29 -12.27 167.41 50 4.5 29
## 30 -30.66 180.13 411 4.7 42
## 31 -23.47 180.21 553 4.2 23
## 32 -23.31 179.27 566 5.1 49
## 33 -13.62 167.15 209 4.7 30
## 34 -23.44 184.60 63 4.8 27
## 35 -20.91 181.57 530 4.2 20
## 36 -17.59 181.09 536 5.1 61
## 37 -21.60 169.90 43 5.2 56
## 38 -13.23 167.10 220 5.0 46
## 39 -16.20 166.80 98 4.5 21
## 40 -13.84 170.62 638 4.6 20
## 41 -33.29 181.30 60 4.7 33
## 42 -21.60 180.50 595 4.0 22
## 43 -17.46 181.42 524 4.2 16
## 44 -18.14 181.71 574 4.0 20
## 45 -15.80 185.25 82 4.4 39
## 46 -23.30 180.16 512 4.4 18
## 47 -17.98 181.61 598 4.3 27
## 48 -21.38 181.39 501 4.6 36
## 49 -21.30 180.82 624 4.3 14
## 50 -24.97 179.54 505 4.9 50
## 51 -23.47 179.95 543 4.1 21
## 52 -20.37 182.10 397 4.2 22
## 53 -34.20 179.43 40 5.0 37
## 54 -26.67 182.40 186 4.2 17
## 55 -20.60 182.28 529 5.0 50
## 56 -15.90 167.16 41 4.8 42
## 57 -19.86 184.35 201 4.5 30
## 58 -24.96 179.87 480 4.4 25
## 59 -18.18 182.04 609 4.4 26
## 60 -12.66 169.46 658 4.6 43
## 61 -17.91 181.48 555 4.0 17
## 62 -12.01 166.66 99 4.8 36
## 63 -30.01 181.15 210 4.3 17
## 64 -23.83 182.56 229 4.3 24
## 65 -25.31 179.69 507 4.6 35
## 66 -23.33 180.18 528 5.0 59
## 67 -17.40 187.80 40 4.5 14
## 68 -37.37 176.78 263 4.7 34
## 69 -18.40 183.40 343 4.1 10
## 70 -15.41 186.44 69 4.3 42
## 71 -17.40 181.02 479 4.4 14
## 72 -22.43 184.48 65 4.9 48
## 73 -13.26 167.01 213 5.1 70
## 74 -26.13 178.31 609 4.2 25
## 75 -32.82 179.80 176 4.7 26
## 76 -21.63 180.77 592 4.3 21
## 77 -30.51 181.30 203 4.4 20
## 78 -15.03 167.32 136 4.6 20
## 79 -17.02 182.93 406 4.0 17
## 80 -18.78 186.72 68 4.8 48
## 81 -17.66 181.40 585 4.1 17
## 82 -20.90 169.84 93 4.9 31
## 83 -21.29 185.77 57 5.3 69
## 84 -30.28 180.62 350 4.7 32
## 85 -22.70 170.30 69 4.8 27
## 86 -17.95 181.37 642 4.0 17
## 87 -23.55 180.80 349 4.0 10
## 88 -15.17 187.20 50 4.7 28
## 89 -18.54 182.11 554 4.4 19
## 90 -20.42 181.86 530 4.5 27
## 91 -17.74 181.25 559 4.1 16
## 92 -24.41 180.03 500 4.5 34
## 93 -23.61 180.23 475 4.4 26
## 94 -22.00 180.53 583 4.9 20
## 95 -24.78 179.22 492 4.3 16
## 96 -15.43 186.30 123 4.2 16
## 97 -17.70 181.31 549 4.7 33
## 98 -18.48 181.49 641 5.0 49
## 99 -22.10 179.71 579 5.1 58
## 100 -18.10 181.63 592 4.4 28
## 101 -24.40 179.85 522 4.7 29
## 102 -17.80 181.32 539 4.1 12
## 103 -14.65 166.97 82 4.8 28
## 104 -36.95 177.81 146 5.0 35
## 105 -24.81 180.00 452 4.3 19
## 106 -11.49 166.22 84 4.6 32
## 107 -22.70 183.30 180 4.0 13
## 108 -37.93 177.47 65 5.4 65
## 109 -19.60 185.20 125 4.4 13
## 110 -15.45 186.73 83 4.7 37
## 111 -20.14 181.60 587 4.1 13
## 112 -18.14 180.87 624 5.5 105
## 113 -25.63 180.26 464 4.8 60
## 114 -17.70 181.70 450 4.0 11
## 115 -35.48 179.90 59 4.8 35
## 116 -15.48 186.73 82 4.4 17
## 117 -18.75 182.35 554 4.2 13
## 118 -23.74 179.99 506 5.2 75
## 119 -17.42 185.16 206 4.5 22
## 120 -16.90 185.72 135 4.0 22
## 121 -23.54 179.93 574 4.0 12
## 122 -33.03 180.20 186 4.6 27
## 123 -11.41 166.24 83 5.3 55
## 124 -18.76 169.71 287 4.4 23
## 125 -19.30 183.84 517 4.2 21
## 126 -16.17 184.10 338 4.3 13
## 127 -18.69 169.10 218 4.2 27
## 128 -15.00 184.62 40 5.1 54
## 129 -23.73 183.00 118 4.3 11
## 130 -32.62 181.50 55 4.8 26
## 131 -38.59 175.70 162 4.7 36
## 132 -14.70 166.00 48 5.3 16
## 133 -21.40 180.78 615 4.7 51
## 134 -21.35 170.04 56 5.0 22
## 135 -26.00 178.43 644 4.9 27
## 136 -19.06 182.45 477 4.0 16
## 137 -18.07 181.54 546 4.3 28
## 138 -13.80 166.53 42 5.5 70
## 139 -23.34 184.50 56 5.7 106
## 140 -18.21 180.87 631 5.2 69
## 141 -19.60 181.87 597 4.2 18
## 142 -19.10 184.52 230 4.1 16
## 143 -11.34 166.24 103 4.6 30
## 144 -20.36 186.16 102 4.3 21
## 145 -15.54 167.68 140 4.7 16
## 146 -18.56 169.05 217 4.9 35
## 147 -20.42 181.96 649 4.0 11
## 148 -26.10 182.30 49 4.4 11
## 149 -20.40 186.10 74 4.3 22
## 150 -19.13 182.51 579 5.2 56## [1] 4.58## [1] 0.03288628Z_valor <- qnorm(0.95)
margen_error <- Z_valor * SE_media
# limites de intervalo
limite_inf<- media_muestral - margen_error
limite_sup <- media_muestral + margen_error
cat("Valor Z (90%):", round(Z_valor, 3), "\n")## Valor Z (90%): 1.645## Margen de Error: 0.0541cat("Intervalo de Confianza (90%) para la media de magnitud:",
round(limite_inf, 3), " a ", round(limite_sup, 3), "\n")## Intervalo de Confianza (90%) para la media de magnitud: 4.526 a 4.634#Proporcion
P_poblacional <- poblacion %>%
mutate(grave = ifelse(mag >= 5.0, 1, 0)) %>%
summarise(P = mean(grave)) %>%
pull(P)
cat("Proporción Poblacional de Sismos Graves (P):", round(P_poblacional, 4), "\n")## Proporción Poblacional de Sismos Graves (P): 0.198p_muestral <- muestra %>%
mutate(grave = ifelse(mag >= 5.0, 1, 0)) %>%
summarise(p = mean(grave)) %>%
pull(p)
cat("Proporción Muestral de Sismos Graves (p):", round(p_muestral, 4), "\n")## Proporción Muestral de Sismos Graves (p): 0.2SE_proporcion <- sqrt( (P_poblacional * (1 - P_poblacional)) / n_muestra )
cat("Error Estándar de la Proporción Muestral (SE_p):", round(SE_proporcion, 4), "\n")## Error Estándar de la Proporción Muestral (SE_p): 0.0325