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--- c:mrm:2026:schedule:w07_note [2026/04/13 01:13] – hkimscil
+++ c:mrm:2026:schedule:w07_note [2026/04/16 01:16] (current) – hkimscil
@@ Line 13: / Line 13: @@
   * [[:r:hypothesis testing]]
+<tabbox rs.sampling.distribution.with.many.ns>
+<code>
+m.p <- 100
+sigma <- 10
+se.4 <- sigma / sqrt(4)
+se.16 <- sigma / sqrt(16)
+se.25 <- sigma / sqrt(25)
+se.100 <- sigma / sqrt(100)
+se.400 <- sigma / sqrt(400)
+se.900 <- sigma / sqrt(900)
+se.1600 <- sigma / sqrt(1600)
+se.10000 <- sigma /sqrt(10000)
+curve(dnorm(x, m.p, se.900), from = 80, to = 120,
+      main = "normalized distribution of sample means",
+      ylab = "Density", xlab = "z-value", col = "black", lwd = 2)
+curve(dnorm(x, m.p, se.400), from = 80, to = 120,
+      main = "normalized distribution of sample means",
+      ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+curve(dnorm(x, m.p, se.100), from = 80, to = 120,
+      main = "normalized distribution of sample means",
+      ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+curve(dnorm(x, m.p, se.25), from = 80, to = 120,
+      main = "normalized distribution of sample means",
+      ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+curve(dnorm(x, m.p, se.16), from = 80, to = 120,
+      main = "normalized distribution of sample means",
+      ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+abline(v=m.p, col="red", lwd=2)
+se.10000
+se.1600
+se.900
+se.400
+se.100
+se.25
+se.16
+c(m.p-se.10000*2, m.p+se.10000*2)
+c(m.p-se.1600*2, m.p+se.1600*2)
+c(m.p-se.900*2, m.p+se.900*2)
+c(m.p-se.400*2, m.p+se.400*2)
+c(m.p-se.100*2, m.p+se.100*2)
+c(m.p-se.25*2, m.p+se.25*2)
+c(m.p-se.16*2, m.p+se.16*2)
+</code>
+<tabbox ro.sampling.distribution.with.many.ns>
+<code>
+> m.p <- 100
+> sigma <- 10
+>
+> se.4 <- sigma / sqrt(4)
+> se.16 <- sigma / sqrt(16)
+> se.25 <- sigma / sqrt(25)
+> se.100 <- sigma / sqrt(100)
+> se.400 <- sigma / sqrt(400)
+> se.900 <- sigma / sqrt(900)
+> se.1600 <- sigma / sqrt(1600)
+> se.10000 <- sigma /sqrt(10000)
+>
+> curve(dnorm(x, m.p, se.900), from = 80, to = 120,
++       main = "normalized distribution of sample means",
++       ylab = "Density", xlab = "z-value", col = "black", lwd = 2)
+> curve(dnorm(x, m.p, se.400), from = 80, to = 120,
++       main = "normalized distribution of sample means",
++       ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+> curve(dnorm(x, m.p, se.100), from = 80, to = 120,
++       main = "normalized distribution of sample means",
++       ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+> curve(dnorm(x, m.p, se.25), from = 80, to = 120,
++       main = "normalized distribution of sample means",
++       ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+> curve(dnorm(x, m.p, se.16), from = 80, to = 120,
++       main = "normalized distribution of sample means",
++       ylab = "Density", xlab = "z-value", col = "black", lwd = 2, add=T)
+> abline(v=m.p, col="red", lwd=2)
+>
+> se.10000
+[1] 0.1
+> se.1600
+[1] 0.25
+> se.900
+[1] 0.3333333
+> se.400
+[1] 0.5
+> se.100
+[1] 1
+> se.25
+[1] 2
+> se.16
+[1] 2.5
+>
+> c(m.p-se.10000*2, m.p+se.10000*2)
+[1]  99.8 100.2
+> c(m.p-se.1600*2, m.p+se.1600*2)
+[1]  99.5 100.5
+> c(m.p-se.900*2, m.p+se.900*2)
+[1]  99.33333 100.66667
+> c(m.p-se.400*2, m.p+se.400*2)
+[1]  99 101
+> c(m.p-se.100*2, m.p+se.100*2)
+[1]  98 102
+> c(m.p-se.25*2, m.p+se.25*2)
+[1]  96 104
+> c(m.p-se.16*2, m.p+se.16*2)
+[1]  95 105
+</code>
+{{.:pasted:20260416-011623.png}}
+</tabbox>