Z1CriticalValue <- function(alpha,tails=2){
crit = qnorm(1-alpha/abs(tails))
if(tails==2 || tails==1 )return(crit)
if(tails==-1)return(-crit) else return(NA)
}

########

Z1CriticalValue(0.05,2)
Z1CriticalValue(0.05,-1)

#####

Z1CriticalValue(0.05,1)
1 - pnorm(Z1CriticalValue(0.05,1),2.5,1)

#######

power.onesample.z <- function(mu,mu0,sigma,n,alpha,tails=2){
 Es <- (mu-mu0)/sigma
 R <- Z1CriticalValue(alpha,tails)
 m <- sqrt(n)*abs(Es) - abs(R)
 return(pnorm(m))
 }
power.onesample.z(75,70,10,25,0.05,1)

######################

curve(power.onesample.z(75,70,10,x,.05,1),20,60,xlab="n",ylab="Power")
abline(h=.95,col="red")

######################

n <- 40:45
power <- power.onesample.z(75,70,10,n,.05,1)
cbind(n,power)


####################

curve(power.onesample.z(75,70,10,x,.05,1),40,50,xlab="n",ylab="Power")
abline(h=.95,col="red")
abline(v=42)
abline(v=43)
abline(v=44)

###################

Required.n.Z1 <- function(mu,mu0,sigma,alpha,power,tails){
Es <- (mu-mu0)/sigma
R <- Z1CriticalValue(alpha,tails)
n <- ((qnorm(1-alpha/tails)+qnorm(power))/(abs(Es)))^2
n <- ceiling(n)
return(c(n,power.onesample.z(mu,mu0,sigma,n,alpha,tails)))
}
Required.n.Z1(75,70,10,.05,.95,1)

###################

Required.n.Z1(0.20,0,1,0.01,0.90,2)