#Compute Power of a Hypothesis Test with Known Population Variance
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par(mfrow=c(2,2),oma=c(0,0,5,0))
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n=50
sigma=.035
SE=sigma/sqrt(n)
mu0=.25
mu=.25
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Tail="Left"
#Tail="Right"
#Tail="Both"
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z=seq(-4,4,.01)
plot(z,dnorm(z,mean=0,sd=1),ylab="Density",type="l",col="red")
lines(z,dnorm(z,mean=(mu-mu0)/SE,sd=1),col="blue")
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cord.x=c(-4,seq(-4,-1.65,.01),-1.65)
cord.y=c(0,dnorm(seq(-4,-1.65,.01),mean=(mu-mu0)/SE,sd=1),0)
polygon(cord.x,cord.y,col='blue',density=20)
cord.y=c(0,dnorm(seq(-4,-1.65,.01)),0)
polygon(cord.x,cord.y,col='red',density=20,angle=70)
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abline(h=0)
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power=pnorm(-1.645,mean=(mu-mu0)/SE,sd=1)
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title(main=paste("mu=.25, Power=",round(power,3)))
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mu=.24
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Tail="Left"
#Tail="Right"
#Tail="Both"
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z=seq(-4,4,.01)
plot(z,dnorm(z,mean=0,sd=1),ylab="Density",type="l",col="red")
lines(z,dnorm(z,mean=(mu-mu0)/SE,sd=1),col="blue")
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cord.x=c(-4,seq(-4,-1.65,.01),-1.65)
cord.y=c(0,dnorm(seq(-4,-1.65,.01),mean=(mu-mu0)/SE,sd=1),0)
polygon(cord.x,cord.y,col='blue',density=20)
cord.y=c(0,dnorm(seq(-4,-1.65,.01)),0)
polygon(cord.x,cord.y,col='red',density=20,angle=70)
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abline(h=0)
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power=pnorm(-1.645,mean=(mu-mu0)/SE,sd=1)
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title(main=paste("mu=.24, Power=",round(power,3)))
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mu=.23
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Tail="Left"
#Tail="Right"
#Tail="Both"
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z=seq(-4,4,.01)
plot(z,dnorm(z,mean=0,sd=1),ylab="Density",type="l",col="red")
lines(z,dnorm(z,mean=(mu-mu0)/SE,sd=1),col="blue")
#
cord.x=c(-4,seq(-4,-1.65,.01),-1.65)
cord.y=c(0,dnorm(seq(-4,-1.65,.01),mean=(mu-mu0)/SE,sd=1),0)
polygon(cord.x,cord.y,col='blue',density=20)
cord.y=c(0,dnorm(seq(-4,-1.65,.01)),0)
polygon(cord.x,cord.y,col='red',density=20,angle=70)
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abline(h=0)
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power=pnorm(-1.645,mean=(mu-mu0)/SE,sd=1)
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title(main=paste("mu=.23, Power=",round(power,3)))
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mu=.22
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Tail="Left"
#Tail="Right"
#Tail="Both"
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z=seq(-4,4,.01)
plot(z,dnorm(z,mean=0,sd=1),ylab="Density",type="l",col="red")
lines(z,dnorm(z,mean=(mu-mu0)/SE,sd=1),col="blue")
#
cord.x=c(-4,seq(-4,-1.65,.01),-1.65)
cord.y=c(0,dnorm(seq(-4,-1.65,.01),mean=(mu-mu0)/SE,sd=1),0)
polygon(cord.x,cord.y,col='blue',density=20)
cord.y=c(0,dnorm(seq(-4,-1.65,.01)),0)
polygon(cord.x,cord.y,col='red',density=20,angle=70)
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abline(h=0)
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power=pnorm(-1.645,mean=(mu-mu0)/SE,sd=1)
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title(main=paste("mu=.22, Power=",round(power,3)))
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title(paste("
Density of Z Statistic under Null Hypothesis (Red)
and Left-Tailed Alterntative Hypothesis (Blue)
mu0=",mu0,"sigma=",sigma,"n=",n,"alpha=.05"),outer=T)
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