* R
    * pnorm, qnorm, rnorm, dnorm
    * pt, qt, rt, dt
    * <del> pf, qf, rf, df </del> 나중에
  * variance (''var()'')
    * SS / df
  * standard deviation (''sd()'')
    * sqrt(SS/df)
    * 68, 95, 99 % 
  * [[:r:sampling distribution]] 앞부분 pnorm, qnorm 만 보고 t-test summary 문서를 볼 것 (동일)
    * [[:central limit theorem]]
  * [[:t-test summary]]
  * [[: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>