Type I error

Type I ERROR (False Discovery)

One random sample

\(\alpha = .05\) (Critical Values -2.06, 2.06)

population <- rnorm(10000,0,1)

n <- 25

samp <- sample(population,n)

s <- sd(samp)

xbar <- mean(samp)

statt <- (xbar - 0) * sqrt(n)/s

statt

## [1] -2.215578

A few random samples

i  <-  1
nn <- 20
stat  <- vector(mode = "numeric",length = nn)

population <- rnorm(10000,0,1)

for (i in 1:nn) {
        
        samp    <- sample(population,n)

        s       <- sd(samp)

        xbar    <- mean(samp)

        stat[i] <- (xbar - 0) * sqrt(n)/s

        

}


#c(qt(.975,24),qt(.025,24))

stat

##  [1] -0.34462853 -1.03976824  1.24418068 -1.19729368  0.62804099
##  [6] -0.97980862  0.40591786  0.49424022  2.84202132  2.49564472
## [11]  0.91279627  0.13088136  1.08977851 -0.49166765 -1.05058938
## [16] -1.45550732  0.08348907  1.48619378  0.18618938 -0.91987791

#y <-ifelse(stat < -2.06 | stat > 2.06,1,0 )
#sum(y)

#sum(y)/nn