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@ -49,7 +49,7 @@
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paste("Sample size 5: mean = ",
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round(mean(t1$meancol)),
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"; stdev = ",
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round(sqrt(var(t1$meancol))),sep="")->lab
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round(sd(t1$meancol)),sep="")->lab
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p+annotate("text",x=450,y=0.030,label=lab,colour="blue")->p
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p
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@ -67,7 +67,7 @@
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paste("Sample size 20: mean = ",
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round(mean(t0$meancol)),
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"; stdev = ",
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round(sqrt(var(t0$meancol))),sep="")->lab
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round(sd(t0$meancol)),sep="")->lab
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p+annotate("text",x=450,y=0.033,label=lab,colour="darkolivegreen")->p
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p
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@ -85,7 +85,7 @@
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paste("Sample size 50: mean = ",
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round(mean(t$meancol)),
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"; stdev = ",
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round(sqrt(var(t$meancol))),sep="")->lab
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round(sd(t$meancol)),sep="")->lab
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p+annotate("text",x=450,y=0.036,label=lab,colour="red")->p
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p
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@ -103,7 +103,7 @@
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paste("Sample size 200: mean = ",
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round(mean(t4$meancol)),
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"; stdev = ",
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round(sqrt(var(t4$meancol))),sep="")->lab
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round(sd(t4$meancol)),sep="")->lab
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p+annotate("text",x=450,y=0.039,label=lab,colour="pink")->p
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p
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#+end_src
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@ -113,13 +113,14 @@
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+ $Standard.error = \frac{\sigma}{\sqrt{mean}}$
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| Standard deviation of population ($\sigma$) | 130 |
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| Standard errors of samples of size | |
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| 5 | 58 |
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| 20 | 29 |
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| 50 | 18 |
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| 200 | 9 |
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| Variable | Value |
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|---------------------------------------------+-------|
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| Standard deviation of population ($\sigma$) | 130 |
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| Standard errors of samples of size | |
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| 5 | 58 |
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| 20 | 29 |
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| 50 | 18 |
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| 200 | 9 |
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@ -140,7 +141,7 @@
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library(ggplot2)
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worker->t9
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(t9$wage-mean(t9$wage))/sqrt(var(t9$wage))->t9$wage
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(t9$wage-mean(t9$wage))/sd(t9$wage)->t9$wage
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ggplot(t9,aes(wage))+geom_density(colour="black",size=1)->p
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p+scale_y_continuous(limits=c(0,0.75))->p
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p+scale_x_continuous(limits=c(-15,15)
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@ -159,7 +160,7 @@
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c(t1,mean(s1$wage))->t1
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}
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data.frame(sno=c(1:10000),meancol=(t1-mean(worker$wage))/sqrt(var(t1)))->t1
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data.frame(sno=c(1:10000),meancol=(t1-mean(worker$wage))/sd(t1))->t1
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p+geom_density(data=t1,aes(meancol),colour="blue",size=1)-> p
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p
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@ -172,7 +173,7 @@
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c(t0,mean(s1$wage))->t0
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}
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data.frame(sno=c(1:10000),meancol=(t0-mean(worker$wage))/sqrt(var(t0)))->t0
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data.frame(sno=c(1:10000),meancol=(t0-mean(worker$wage))/sd(t0))->t0
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p+geom_density(data=t0,aes(meancol),colour="darkolivegreen",size=1)-> p
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p
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@ -185,7 +186,7 @@
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c(t,mean(s1$wage))->t
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}
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data.frame(sno=c(1:10000),meancol=(t-mean(worker$wage))/sqrt(var(t)))->t
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data.frame(sno=c(1:10000),meancol=(t-mean(worker$wage))/sd(t))->t
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p+geom_density(data=t,aes(meancol),colour="red",size=1)-> p
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p
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@ -198,7 +199,7 @@
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c(t4,mean(s1$wage))->t4
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}
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data.frame(sno=c(1:10000),meancol=(t4-mean(worker$wage))/sqrt(var(t4)))->t4
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data.frame(sno=c(1:10000),meancol=(t4-mean(worker$wage))/sd(t4))->t4
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p+geom_density(data=t4,aes(meancol),colour="pink",size=1)-> p
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p
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#+end_src
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@ -220,7 +221,7 @@
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worker[sex!=3,]->worker
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worker->t9
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(t9$wage-mean(t9$wage))/sqrt(var(t9$wage))->t9$wage
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(t9$wage-mean(t9$wage))/sd(t9$wage)->t9$wage
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ggplot(t9,aes(wage))+geom_density(colour="black",size=1)->p
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p+scale_y_continuous(limits=c(0,0.75))->p
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p+scale_x_continuous(limits=c(-15,15)
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@ -236,19 +237,19 @@
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rbind(t4,data.frame(
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sno=i,
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meancol=mean(s1$wage),
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sterr=sqrt(var(s1$wage))/sqrt(samplesize)
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sterr=sd(s1$wage)/sqrt(samplesize)
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)
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)->t4
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}
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(t4$meancol)/t4$sterr->t4$teststat
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(t4$meancol)/sqrt(var(t4$meancol))->t4$teststat2
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(t4$meancol)/sd(t4$meancol)->t4$teststat2
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data.frame(modelt=rt(200000,samplesize-1,ncp=mean(t4$teststat)),modelnorm=rnorm(200000,mean=mean(t4$teststat2)))->m
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var(t4$teststat)
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var(m$modelt)
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var(m$modelnorm)
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var(t4$teststat2)
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sd(t4$teststat)
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sd(m$modelt)
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sd(m$modelnorm)
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sd(t4$teststat2)
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mean(t4$teststat)
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mean(m$modelt)
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mean(m$modelnorm)
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@ -260,18 +261,18 @@
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p+geom_density(data=t4,aes(teststat),colour="blue",size=1)-> p
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p+geom_density(data=m,aes(modelt),colour="darkolivegreen",size=1)->p
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p+annotate("text",x=-30,y=0.42,
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label=paste("Normal distribution, with standard deviation",round(sqrt(var(m$modelnorm)),2)),
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label=paste("Normal distribution, with standard deviation",round(sd(m$modelnorm),2)),
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colour="black",hjust=0)->p
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p+annotate("text",x=-30,y=0.40,
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label=paste("Statistic with known population variance, standard error =",
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round(sqrt(var(t4$teststat2)),2)),
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round(sd(t4$teststat2),2)),
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colour="red",hjust=0)->p
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p+annotate("text",x=-30,y=0.38,
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label=paste("t distribution, with standard deviation =",round(sqrt(var(m$modelt)),2)),
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label=paste("t distribution, with standard deviation =",round(sd(m$modelt),2)),
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colour="darkolivegreen",hjust=0)->p
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p+annotate("text",x=-30,y=0.36,
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label=paste("Statistic with unknown population variance, standard error =",
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round(sqrt(var(t4$teststat)),2)),
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round(sd(t4$teststat),2)),
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colour="blue",hjust=0)->p
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p+scale_x_continuous(limits=c(-30,30))+theme_bw()->p
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p
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