Design and Analysis of Experiment

x <- c(15.3 ,-31.8 ,-35.6 ,-14.5 ,3.1 ,-24.5)
#random 
r <- function(){ 
  sample(x = c(1,-1),size = 6,replace = T,prob = c(0.5,0.5))
}
#
t <- function(e){
  sum(e)/sd(e)
}
#experiment
exp <- NULL
for(i in 1:10000){
  a <- t(x*r())
  exp[i] <- a
}
hist(exp,breaks = 64,main = "obs of random experiment")

p <- (sum(t(x)>exp)+sum((-1)*t(x)<exp))/10000
p  #0.0795

## [1] 0.1559

#p <0.05 >>> reject H0 under alpha = 0.05
#insecticide chlordane has affected the (Na+ ,-K+ ,ATPas) activity.

o <- c(0.950, 0.978, 0.762, 0.733, 0.823, 1.011)
r <- function(){ 
  sample(x = c(1,0),size = 6,replace = T,prob = c(0.5,0.5))
}
#experiment
exp <- NULL
for (i in 1:10000) {
  x <- c(0.950, 0.978, 0.762, 0.733, 0.823, 1.011)
  a <- r()
  for (j in 1:6) {
    if(a[j] == 0){ x[j] <- (1/x[j]) 
    }
  }
  exp[i] <- sum(x)
}
hist(exp , breaks = 64)

p <- sum(sum(o)<exp)/10000
p

## [1] 0.9677

#p <0.05 >>> reject H0 under alpha = 0.05
#Visiplume reads higher than the standard