#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
# Computations used for the problems in this section of the text.
#
#-----

# 7.12
#
n = 110
m = 0.81
s = 0.34
z_crit = qnorm( 1 - 0.01/2 )
m + (s/sqrt(n)) * z_crit * c(-1,+1)

# 7.13
#
n = 50
m = 654.16
s = 164.43
z_crit = qnorm( 1 - 0.05/2 )
m + (s/sqrt(n)) * z_crit * c(-1,+1)

s = 175
z_alpha_over_two = qnorm( 1 - 0.05/2 )
w = 50 # the desired width 
( 2 * s * z_alpha_over_two / w )^2 

# 7.14
#
n = 169
xbar = 89.10
s = 3.73

alpha = 0.05
z_crit = qnorm( 1 - alpha/2 )
xbar + ( s / sqrt(n) ) * z_crit * c(-1,+1)

( 2 * ( s/sqrt(n) ) * z_crit ) / xbar # the fractional width 

w = 0.5
s = 4
( ( 2 * s * z_crit ) / w )^2