# typical hours/week spent on HW STAT 205H, Fall 2017
h=c(22,15,7,10,10,15,14,10,20,20,5,14,20,10,5,10,15,3)

m=length(h)      # population size
n=5              # sample size

# compute one mean of size n=5
ybar=0
for(j in 1:n){
 index=ceiling(runif(1)*m)
 cat("Student",index,"spends",h[index],"hours. \n")
 ybar=ybar+h[index]}
cat("Mean of all",n,"is ybar =",ybar/n,"hours. \n")

cat("Population mean is ",mean(h),"hours. \n")

# make histogram of 1000 sample ybar's, each n=5
total=1000
mu=mean(h)
means=rep(0,total)
for(i in 1:total){
 ybar=0
 for(j in 1:n){ybar=ybar+h[ceiling(runif(1)*m)]}
 ybar=ybar/n
 means[i]=ybar
}

par(mfrow=c(2,1))
hist(h,freq=FALSE,main="Population density",xlim=c(0,25),xlab="HW hours")
lines(density(h),col="blue")
hist(means,freq=FALSE,xlim=c(min(h),max(h)),main="Density of ybar for n=5")
x=seq(0,20,length=1000)
lines(x,dnorm(x,mean(h),sd(h)/sqrt(n)),col="blue")

# use 5 randomly selected students to make CI for mu=mean in class

t.test(sample(h,5,replace=T))

# use all 18 randomly students to make CI for mu=mean among honors students

t.test(h)