#  Lifetimes in hours of a sample of n=40 
#  Brand A light bulbs 

 xa <- c(64, 70, 76, 92, 150, 152, 193, 228,
         335, 348, 355, 406, 423, 450, 452,  
         461, 592, 658, 665, 689, 704, 744, 874,  
         964, 985, 1053, 1153, 1223, 1352, 1359,
         1386, 1395, 1621, 1845, 2142, 2152,
         2451, 2780, 4479, 4992)

 
# Compute sample mean and sample standard deviation

   xamean <- mean(xa)
   xamean

   xastd <- sqrt(var(xa))
   xastd

# Examine a histogram of the data


frame( )
par(fin=c(8,8),cex=1.2)
   lab <- "Lifetimes (hours) of 40 Brand A Light Bulbs"
   hist(xa, nclass=8, main=lab)


# Estimate the median lifetime

  xa50 <- quantile(xa, 0.5)
  xa50 

# Obtain 1000 bootstrap replicates of the
# estimate of the median from a samples of
# size 40 

 ya <- bootstrap(xa, median, 1000)

 summary(ya)

#  Construct a histogram

   par(fin=c(8,8),cex=1.2)
   lab <- "1000 Bootstrap Median Estimates (n=40)"
   hist(ya$replicates, nclass=20, main=lab)

   
#  Lifetimes in hours of a sample of n=40 
#  Brand B light bulbs 

 xb <- c(4, 23, 44, 47, 61, 63, 70, 114, 120, 123,
         192, 201, 245, 250, 258, 261, 275, 281,  
         307, 347, 392, 400, 412, 461, 484, 572,  
         605, 717, 916, 1078, 1082, 1173, 1259, 
         1401, 1426, 1433, 1640, 1773, 1937, 2794)

# Compute sample mean and sample standard deviation

   xbmean <- mean(xb)
   xbmean

   xbstd <- sqrt(var(xb))
   xbstd

# Examine a histogram of the data


frame( )
par(fin=c(8,8),cex=1.2)
   lab <- "Lifetimes (hours) of 40 Brand B Light Bulbs"
   hist(xb, nclass=8, main=lab)


# Estimate the median lifetime

  xb50 <- quantile(xb, 0.5)
  xb50   

# Obtain 1000 bootstrap replicates of the
# estimate of the median from a samples of
# size 40 

 yb <- bootstrap(xb, median, 1000)

 summary(yb)


#  Construct a histogram

   par(fin=c(8,8),cex=1.2)
   lab <- "1000 Bootstrap Median Estimates (n=40)"
   hist(yb$replicates, nclass=20, main=lab)


# Obtain a confidence interval for the difference
# in the medain lifetimes for the two brands
# of light bulbs.

   quantile(ya$replicates-yb$replicates, c(0.025, 0.975))


#  Construct a histogram of the bootstrap differences
#  in estimates of median lifetimes

   par(fin=c(8,8),cex=1.2)
   lab <- "1000 Bootstrap Differences in Medians"
   hist(ya$rep-yb$rep, nclass=20, main=lab)