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--- note.w02 [2025/09/12 19:38] – [9] hkimscil
+++ note.w02 [2025/09/12 19:39] (current) – [Sampling Distribution and z-test] hkimscil
@@ Line 23: / Line 23: @@
 sd(p1)
-p2 <- rnorm2(N.p, m.p+5, sd.p)
+p2 <- rnorm2(N.p, m.p+20, sd.p)
 mean(p2)
 sd(p2)
@@ Line 31: / Line 31: @@
 var(p1)
+hist(p1)
 hist(p1, breaks=50, col = rgb(1, 1, 1, 0.5),
      main = "histogram of p1 and p2",)
@@ Line 41: / Line 41: @@
 hist(p1, breaks=50, col=rgb(0,.5,.5,.5))
 abline(v=mean(p1),lwd=2)
-abline(v=mean(p1)-sd(p1), lwd=2)
+abline(v=m.p1-sd.p1, lwd=2)
 abline(v=mean(p1)+sd(p1), lwd=2)
 abline(v=c(m.p1-2*sd.p1, m.p1+2*sd.p1), lwd=2, col='red')
@@ Line 60: / Line 60: @@
 pnorm(m.p1+3*sd.p1, m.p1, sd.p1) -
   pnorm(m.p1-3*sd.p1, m.p1, sd.p1)
+pnorm(121, 100, 10) - pnorm(85, 100, 10)
 m.p1
@@ Line 69: / Line 71: @@
 pnorm(1)-pnorm(-1)
 pnorm(2)-pnorm(-2)
-pnorm(3)-pnorm(3)
+pnorm(3)-pnorm(-3)
 -pnorm(-2)*2
@@ Line 154: / Line 156: @@
 ################################
-s.size <- 50
+s.size <- 10
 means.temp <- c()
@@ Line 199: / Line 201: @@
 se.z <- sqrt(var(p1)/s.size)
+se.z
 se.z <- c(se.z)
 se.z
@@ Line 301: / Line 304: @@
 sd(means)
-tmp <- mean(means) - (m.s.from.p2 - mean(means))
+m.k <- mean(s.from.p2)
+se.k <- sd(s.from.p2)/sqrt(s.size)
+tmp <- mean(means) - (m.s.from.p2
+                    - mean(means))
 tmp
@@ Line 315: / Line 323: @@
 m.s.from.p2
 pnorm(m.s.from.p2, mean(p1), se.z, lower.tail = F)
+pnorm(m.s.from.p2, m.k, se.k, lower.tail = F)
 # then, what is the probabilty of getting
 # greater than m.sample.i.got and
@@ Line 323: / Line 331: @@
 abline(v=tmp, col='red', lwd=3)
 * pnorm(m.s.from.p2, mean(p1), se.z, lower.tail = F)
+* pnorm(m.s.from.p2, m.k, se.k, lower.tail = F)
 se.z
@@ Line 338: / Line 349: @@
 pt(z.cal, 49, lower.tail = F)*2
 t.test(s.from.p2, mu=mean(p1), var.equal = T)
 </code>