### Class examples from Week 6: Samples and Populations
### Ken Benoit Feb 2010


## Levin and Fox Table 6.1 example
pop <- c(70, 86, 56, 40, 89, 99, 96, 80, 85, 52,
         78, 49, 72, 94, 93, 90, 67, 57, 48, 30)
(mu <- mean(pop))
(s1 <- sample(pop, 4))
mean(s1)
(s2 <- sample(pop, 4))
mean(s2)
(s3 <- sample(pop, 4))
mean(s3)


## Step-by-step illustration LF&F pp197-199
x <- c(1,5,2,3,4,1,2,2,4,3)
mean(x)                       # step 1
(s <- sd(x))                  # step 2
(s <- sqrt(sum(x^2)/10 - mean(x)^2)) # step 2 population version from L&F
n <- length(x)                # step 3
(sxbar <- s/sqrt(n-1))
(tval <- qt(1-.05/2, 9))      # step 4: t-critical value
(me <- sxbar * tval)          # step 5: margin of error
c(mean(x)-me, mean(x)+me)     # step 6: 95% confidence interval

(tval99 <- qt(1-.01/2, 9))    # same computation for 99% CI
(me <- sxbar * tval99)        # margin of error
c(mean(x)-me, mean(x)+me)     # 95% confidence interval

t.test(x)   # easier way to get t-distribution 95% CI
t.test(x, conf.level=.99)  # 99% CI