hypothesis2

R Markdown

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] -0.9144907

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]  1.16848790  1.05989927 -1.14122647  0.92402982  0.29416506
##  [6] -0.50320707  0.10773201  0.06908419 -3.46086189  0.32127860
## [11]  1.94513215 -1.14547302 -0.97822428  0.31331169 -0.48584174
## [16]  0.90856659  0.28051002  0.05362874  0.70343271  0.24897659

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

#sum(y)/nn