#21

 X <- read.csv("umpires.csv", header = TRUE)
 n <- length(X[,1])
			 # this trick will do subsetting
 Y1unc <- X[X[,2] == 0,1] 
 Y2unc <- X[X[,2] == 0,3] 

 boxplot(Y1unc, Y2unc)
 t.test(Y1unc, Y2unc)    # this is wrong on two levels:  
   #   1) the variances are widely different  
   #   2) the samples are not independent!

 plot(Y2unc, Y1unc)
   cor(Y2unc, Y1unc) 

## correct way

 Y <- X[,1] - X[,3]       # we recognize this as a paired sample 

 #  Y <- X[,1]/X[,3]   another possibility
                        
 Yunc <- Y1unc - Y2unc          # only uncensored data
 hist(Yunc)

 t.test(Yunc)               # this test is invalid, however, due to censoring 
 wilcox.test(Yunc)

 # t.test(Yunc, mu = 1)           # these are for Y <- X[,1]/X[,3]  option 
 # wilcox.test(Yunc, mu = 1)



#22

y1 <- c(5.79, 1579.52, 2323.70) 
y2 <- c(68.8, 108.29, 110.29, 426.07, 1067.60)    # these are ridiculously accurate! 

y1 <- log(y1) 
y2 <- log(y2) 

sp <- sqrt( (var(y1)*2 + var(y2)*4 )/6) 
print(sp)



#26
X <- read.csv("dioxin.csv", header = TRUE) 
logD <- log(X[,1]+0.5)    
boxplot(logD ~ X[,2])

t.test(logD ~ X[,2], var.equal = TRUE)    # this option will perform the "pooled" t-test favored by the book  


#32

X <- read.csv("tuition_3-32.csv", header = TRUE) 
par(mfrow =c(1,2))    # will create two plots in the same window
boxplot(X[,1], X[,2], X[,3])

X <- log(X)
boxplot(X[,1], X[,2], X[,3])    # this is done for a multiplicative effect

   # part (a) 
 t.test(X[,3], X[,2], paired=TRUE)
 exp(c(0.926, 1.224))   # this is the C.I. for the ratio  
     # out of state: in state is  2.52 to 3.40 times
 

 plot(X[,2], X[,3])                 
 lines( c(0,mean(X[,2])), c(0, mean(X[,3])) )
      # this is a naive fit for the X3 = X*beta equation
 plot(exp(X[,2]), exp(X[,3]), xlim=c(0,3500), ylim=c(0,10000))       # however, original data could also follow a linear relationship 
 plot(exp(X[,2]), exp(X[,3]))

 # part (b)
  t.test(X[,1], X[,3])
 exp(c(0.339, 0.804))   # this is the C.I. for the ratio  
     # private: public(out of state) is  1.40 to 2.23 times