nhl_ht_wt <- read.csv("http://www.stat.ufl.edu/~winner/data/nhl_ht_wt.csv", header=T) attach(nhl_ht_wt); names(nhl_ht_wt) bmi <- 703*Weight/(Height^2) (mu.bmi <- mean(bmi)) (sigma.bmi <- sd(bmi)) (N.bmi <- length(bmi)) n.sim <- 10000 z.bmi <- numeric(n.sim) t.bmi <- numeric(n.sim) n.sample <- 16 set.seed(654321) for (i in 1:n.sim) { bmi.sample <- sample(bmi,n.sample,replace=F) z.bmi[i] <- (mean(bmi.sample) - mu.bmi) / (sigma.bmi/sqrt(n.sample)) t.bmi[i] <- (mean(bmi.sample) - mu.bmi) / (sd(bmi.sample)/sqrt(n.sample)) } mean(z.bmi); sd(z.bmi); quantile(z.bmi,c(.025,.975)) mean(t.bmi); sd(t.bmi); quantile(t.bmi,c(.025,.975)) zt.range <- seq(-4,4,.01) hist(z.bmi[(z.bmi >= -4) & (z.bmi <=4)] ,breaks=seq(-4,4,.1),main="histogram of Z w/ N(0,1)") lines(zt.range,dnorm(zt.range,0,1)*n.sim*0.1) hist(t.bmi[(t.bmi >= -4) & (t.bmi <=4)] ,breaks=seq(-4,4,.1),main="histogram of t w/ N(0,1)") lines(zt.range,dnorm(zt.range,0,1)*n.sim*0.1) hist(t.bmi[(t.bmi >= -4) & (t.bmi <=4)] ,breaks=seq(-4,4,.1),main="histogram of t with t(16-1)") lines(zt.range,dt(zt.range,n.sample-1)*n.sim*0.1)