Math32lab

#Exercise1
par(mfrow=c(1,2));
stdv<-sqrt(20);
var=20
n=50

X<-rnorm(50, mean=71,sd=stdv);
mean(X);
z<-(mean(X)-70)/(sqrt(var/n));
p <- pnorm(-abs(z),0,1) + 1 - pnorm(abs(z),0,1);
hist(X);


#Exercise2
var=(1/49)*sum((mean(X)-X)^2);
X1<-rnorm(50, mean=71,sd=stdv);
mean(X1);
z1<-(mean(X)-70)/(sqrt(var/n));
p1 <- pnorm(-abs(z1),0,1) + 1 - pnorm(abs(z1),0,1);
hist(X1);

#Exercise3
p2<- pt(-abs(z),49)+1-pt(z,49);
print(c(p,p1,p2));