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--- sampling_distribution_in_r [2024/03/20 08:23] – hkimscil
+++ sampling_distribution_in_r [2024/03/20 14:15] (current) – [Sampling distribution in R e.g. 1] hkimscil
@@ Line 1: / Line 1: @@
 ====== Sampling distribution in R e.g. 1 ======
 <code>
-n.ajstu <- 1000000
+n.ajstu <- 100000
-mean.ajstu <- 70
+mean.ajstu <- 100
 sd.ajstu <- 10
 set.seed(1024)
 ajstu <- rnorm2(n.ajstu, mean=mean.ajstu, sd=sd.ajstu)
@@ Line 9: / Line 10: @@
 mean(ajstu)
 sd(ajstu)
-iter <- 10000
+var(ajstu)
+iter <- 10000 # # of sampling
-n <- 4
+n.4 <- 4
 means4 <- rep (NA, iter)
 for(i in 1:iter){
-  means4[i] = mean(sample(ajstu, n))
+  means4[i] = mean(sample(ajstu, n.4))
 }
-n <- 25
+n.25 <- 25
 means25 <- rep (NA, iter)
 for(i in 1:iter){
-  means25[i] = mean(sample(ajstu, n))
+  means25[i] = mean(sample(ajstu, n.25))
 }
-n <- 100
+n.100 <- 100
 means100 <- rep (NA, iter)
 for(i in 1:iter){
-  means100[i] = mean(sample(ajstu, n))
+  means100[i] = mean(sample(ajstu, n.100))
 }
-n <- 400
+n.400 <- 400
 means400 <- rep (NA, iter)
 for(i in 1:iter){
-  means400[i] = mean(sample(ajstu, n))
+  means400[i] = mean(sample(ajstu, n.400))
 }
-n <- 900
+n.900 <- 900
 means900 <- rep (NA, iter)
 for(i in 1:iter){
-  means900[i] = mean(sample(ajstu, n))
+  means900[i] = mean(sample(ajstu, n.900))
 }
-n <- 1600
+n.1600 <- 1600
 means1600 <- rep (NA, iter)
 for(i in 1:iter){
-  means1600[i] = mean(sample(ajstu, n))
+  means1600[i] = mean(sample(ajstu, n.1600))
 }
-n <- 2500
+n.2500 <- 2500
 means2500 <- rep (NA, iter)
 for(i in 1:iter){
-  means2500[i] = mean(sample(ajstu, n))
+  means2500[i] = mean(sample(ajstu, n.2500))
 }
@@ Line 68: / Line 71: @@
 plot(h900, add = T, col="yellow")
-se4 <- sqrt(var(ajstu)/4)
-se25 <- sqrt(var(ajstu)/25)
-se100 <- sqrt(var(ajstu)/100)
-se400 <- sqrt(var(ajstu)/400)
-se900 <- sqrt(var(ajstu)/900)
-se1600 <- sqrt(var(ajstu)/1600)
-se2500 <- sqrt(var(ajstu)/2500)
-sss <- c(4,25,100,400,900,1600,2500)
+sss <- c(4,25,100,400,900,1600,2500) # sss sample sizes
-ses <- rep (NA, length(sss))
+ses <- rep (NA, length(sss)) # std errors
 for(i in 1:length(sss)){
   ses[i] = sqrt(var(ajstu)/sss[i])
 }
+ses
 se.1 <- ses
-se.2 <- 2*ses
+se.2 <- 2 * ses
-lower.part.2 <- mean(ajstu)-se.2
-upper.part.2 <- mean(ajstu)+se.2
-data.frame(cbind(lower.part.2, upper.part.2))
+lower.s2 <- mean(ajstu)-se.2
+upper.s2 <- mean(ajstu)+se.2
+data.frame(cbind(sss, ses, lower.s2, upper.s2))
 </code>
+<code>
+# n =1600 일 경우에
+# sample의 평균이 100.15보다 작을
+# 확률은 어떻게 구해야 할까?
+# n = 1600 일 경우에
+# sampling distribution은
+# Xbar ~ N(100, var(ajstu)/n.1600)
+# 그리고, 위에서 standard error값은
+# sqrt(var(ajstu)/n.1600)
+# 이것을 standard error라고 부른다
+# 따라서
+se.1600 <- sqrt(var(ajstu)/n.1600)
+pnorm(100.15, mean(ajstu), se.1600)
+</code>
 {{:pasted:20240319-120709.png}}
 ===== Sampling distribution in proportion in R =====