Question

Write a simulation in R that shows the distribution of the t-­‐test statistic for a two-­‐sample t test when the null hypothesis is true (i.e. when H0: µ1 -­‐ µ2 = 0 is true). To do this, you should use a for loop that repeatedly performs t-­‐tests comparing sample means of data that come from distributions with the same population mean and standard deviation. Use rnorm() to take samples, t.test() to perform the t-­‐ tests, and use “$statistic” to extract the t-­‐test statistic from the t.test() procedure (e.g. t.test(x,y)$statistic). Make a histogram of the test statistics.

Answer 1

code

solution

#output

#copyable code

#R code

#user set the random seed values

set.seed(123)

#set the mean value by using 2 populations

mu_val<-10

#standard deviation by using 2 populations

sigma_val<-4

#set the number

D<-900

#set the size

num<-20

#initialize the variable by using the statistics process

tstat<-numeric(D)

#using for loop

for (k in 1:D){

#draw a sample using rnorm

sample1<-rnorm(num,mu_val,sigma_val)

#draw a another sample

sample2<-rnorm(num,mu_val,sigma_val)

#store t.test statistics

tstat[k]<-t.test(sample1,sample2)$statistic

}

#draw histogram

hist(tstat,main="Histogram of t-­test statistic",xlab="t stat")