## Read in data, attach file, and print variable names

airq4 <- read.fwf("http://www.stat.ufl.edu/~winner/sta6166/airq4data.txt", 
 width=c(3,6,11,10,6,8,10,8,10),
 col.names=c("city1","city2","pop1","pop2","dist","fare00","pass00","fare01","pass01"))

attach(airq4); names(airq4)

## Create revenue variables for 2000, 2001, and % change variable
rev00 <- 13*fare00*pass00
rev01 <- 13*fare01*pass01
pctchng <- 100*(rev01-rev00)/rev00

## Obtain Summary Stats and histogram for pctchng
summary(pctchng)
hist(pctchng,breaks=50)

## Obtain and print mean, variance, and standard deviation for pctchng
(pct_mean <- mean(pctchng))
(pct_var <- var(pctchng))
(pct_sd <- sd(pctchng))

## Obtain and print out z(.025), the 97.5th %-ile for Z-distribution
(z.025 <- qnorm(.975,0,1))

## Define margin of Error and compute and print Sample size needed
E <- 4
(n.me4 <- (z.025^2*pct_var)/E^2)

## Obtain critical z-value for 1-sided test with alpha=0.05
(z.05 <- qnorm(.95,0,1))
## Compute and print rejection region wrt ybar for n=25
(rr.25 <- -z.05*pct_sd/sqrt(25))
## Compute and print the power (Prob we reject H0 given true mu)
(pow.25 <- pnorm(rr.25,pct_mean,pct_sd/sqrt(25)))

###### Obtain random sample of 50 markets
pct.samp <- sample(pctchng,50,replace=F)

## Compute and print the sample mean and standard deviation
(pct.samp.mean <- mean(pct.samp))
(pct.samp.sd <- sd(pct.samp))

## Compute and print the critical t-value and 95% CI for mu
(t.49.025 <- qt(.975,49))
(pct.samp.ci <- c(pct.samp.mean-t.49.025*pct.samp.sd/sqrt(50),
                  pct.samp.mean+t.49.025*pct.samp.sd/sqrt(50)))

## Compute the t-statistic and lower tail P-value
(pct.samp.ts <- pct.samp.mean/(pct.samp.sd/sqrt(50)))
(pct.samp.pv <- pt(pct.samp.ts,49))