Question 1 STAT2371 Assign

Sample 1

set.seed(8008)
sample_1<-matrix(rnorm(n=100000,mean=-0.5,sd=1),nrow=10000,ncol=10)

function_1<-function(i){
t.test(sample_1[i,],mu=-0.5)$p.value
}

p_value1<-c(1:10000)

for(i in 1:nrow(sample_1)) {
p_value1[i]<-function_1(i)
}

Sample 2

sample_2<-matrix(rnorm(n=100000,mean=0,sd=1),nrow=10000,ncol=10)

function_2<-function(i){
t.test(sample_2[i,],mu=0)$p.value
}

p_value2<-c(1:10000)

for(i in 1:nrow(sample_2)) {
p_value2[i]<-function_2(i)
}

Sample 3

sample_3<-matrix(rnorm(n=100000,mean=0.5,sd=1),nrow=10000,ncol=10)

function_3<-function(i){
t.test(sample_3[i,],mu=0.5)$p.value
}

p_value3<-c(1:10000)

for(i in 1:nrow(sample_3)) {
p_value3[i]<-function_3(i)
}

Sample 4

sample_4<-matrix(rnorm(n=100000,mean=1,sd=1),nrow=10000,ncol=10)

function_4<-function(i){
t.test(sample_4[i,],mu=1)$p.value
}

p_value4<-c(1:10000)

for(i in 1:nrow(sample_4)) {
p_value4[i]<-function_4(i)
}

Histogram’s

par(mfrow=c(2,2))
hist(p_value1,breaks=20, col=5, main="p.value's of sample 1", xlab="p.values")
hist(p_value2,breaks=20, col=2, main= "p.value's of sample 2", xlab="p.values")
hist(p_value3,breaks=20, col=3, main= "p.value's of sample 3", xlab="p.values")
hist(p_value4,breaks=20, col=4, main= "p.value's of sample 4", xlab="p.values")