source('../Chapter6/chap_6_prob_4_data.R')

x_bar = mean(DF$xbar)
print(sprintf('x_bar= %f', x_bar))
s_bar = mean(DF$sigma)
print(sprintf('s_bar= %f', s_bar))

n = 10

# From Table C:
#
A3 = 0.975
B3 = 0.284
B4 = 1.717
LCL_xbar = x_bar - A3*s_bar
UCL_xbar = x_bar + A3*s_bar
cl = c(LCL_xbar, UCL_xbar)
print( sprintf( 'confidence limits xbar= (%f, %f)', cl[1], cl[2] ) )
LCL_range = B3*s_bar
UCL_range = B4*s_bar
cl = c(LCL_range, UCL_range)
print( sprintf( 'confidence limits Rbar= (%f, %f)', cl[1], cl[2] ) )


#postscript("../../WriteUp/Graphics/Chapter6/chap_6_prob_4_plot.eps", onefile=FALSE, horizontal=FALSE)

par(mfrow=c(2,1))

y_lim_min = min( c( DF$xbar, LCL_xbar, UCL_xbar ) )
y_lim_max = max( c( DF$xbar, LCL_xbar, UCL_xbar ) )

plot( DF$xbar, pch=19, ylim=c(y_lim_min, y_lim_max), col='black', ylab='x bars' )
abline(h=x_bar, col='black')
abline(h=c(LCL_xbar, UCL_xbar), col='red', lwd=c(1, 1))
grid()


y_lim_min = min( c( DF$sigma, LCL_range, UCL_range ) )
y_lim_max = max( c( DF$sigma, LCL_range, UCL_range ) )

plot( DF$sigma, pch=19, ylim=c(y_lim_min, y_lim_max), col='black', ylab='sigma' )
abline(h=s_bar, col='black')
abline(h=c(LCL_range, UCL_range), col='red')
grid()

par(mfrow=c(1,1))

#dev.off()

s = s_bar
print(sprintf('sigma= %f', s))
ll = x_bar - 3*s
ul = x_bar + 3*s
print( sprintf( 'confidence limits x= (%f, %f)', ll, ul ) )