#This is a script for Topic 15
#  Know sigma = 9.43.  H0 is mean = 138. 
#  we have             H1 is mean < 138
# we are taking a sample of size 39
# We will do the test at the 0.05 level of significance
#  Critical value approach
#  For a N(0,1) find z such that P( X < z ) = 0.05
qnorm( 0.05 )
#  then use that to find the critical low value
138 + -1.645*9.43/sqrt(39)
#  now use the attained significance approach
pnorm( 135.4, mean=138, sd=9.43/sqrt(39) )
#
#   use the function to solve the problem
source("../hypo_known.R")
hypoth_test_known(138, 9.43, -1, 0.05, 39, 135.4)

#   Next example
#  sigma = 3.94, H0: mean=15.4    H1: mean > 15.4
#  sample size =27    do test a 0.02 level of significance
#
#    critical value method
# for N(0,1) find z such that P(X > z ) = 0.02
qnorm( 0.02, lower.tail=FALSE)
#    then use that to find the critical high value
15.4 + 2.053749 * 3.94/sqrt( 27 )
#    Take the attained significance approach
#    sample mean is 16.9
pnorm( 16.9, mean=15.4, sd=3.94/sqrt(27), lower.tail=FALSE)

#   or just use the function
hypoth_test_known(15.4, 3.94, 1, 0.02, 27, 16.9)

###### example
##  sigma=17.4    H0: mean=143.2      H1: mean != 143.3
##  sample size = 42      alpha = 0.025    
##  mean of sample = 147.1
#
#   critical value first
qnorm(0.025/2)
yl <- 143.2 - 2.241403*(17.4/sqrt(42))
yl
yh <- 143.2 + 2.241403*(17.4/sqrt(42))
yh
#   or the attained significance approach
pnorm( 149.3, mean=143.2, 
       sd=17.4/sqrt(42), lower.tail=FALSE)
#
#   or we could just use the function
hypoth_test_known( 143.2, 17.4, 0, 0.025, 42, 149.3 )
#
#   Example
#     know sigma=23.4      H0: mean= 178    H1:  mean > 178 
#     perform the test at the 0.05 level of significance
#   We take a sample of size 33.  The values in the sample
#   can be generated using gnrnd4
source("../gnrnd4.R")
gnrnd4( 1895433204, 23401873)
L1
x_bar <- mean(L1)
x_bar
hypoth_test_known( 178, 23.4, 37, 0.05, 33, x_bar )