# We have a population of different colored dots.  There
# are 7 different colors and we believe that the proportion
# of each color is 1/7.  We want to test that null 
# hypothesis.
#
# The population of dots is given in the file
#     goodness dots.pdf
#  
# Take a sample of convenience by looking 
# at blocks 600 and 2300.  They are shown in
# the file 
#     blocks of dots.pdf
#
# Then, count the number of each color in our sample.
#    Here is the count of colors
#
#       color |   600  | 2300  |  total
#      -------+--------+-------+--------
#       orange|    16  |   13  |     29
#       purple|    17  |   11  |     28
#       black |     7  |    9  |     16
#       yellow|    12  |   27  |     39
#       green |    20  |    8  |     28
#       blue  |    14  |   16  |     30
#       red   |    14  |   16  |     30
#      -------+--------+-------+--------
#       total |   100  |  100  |    200
#       

# Now do a hypothesis test with the null hypothesis
#     that the proportion of each color is 1/7
#     against the alternative that it is not 1/7
#     and do the test at the 0.05 level of significance.
#   We should not do this because we are just doing
#   multiple tests where we could be doing a single
#   goodness of fit test. However, it is tempting to
#   use a test we had learned before.

source("../hypo_prop.R")
hypoth_test_prop(1/7, 29,200,0,0.05)   # orange
hypoth_test_prop(1/7, 28,200,0,0.05)   # purple
hypoth_test_prop(1/7, 16,200,0,0.05)   # black
hypoth_test_prop(1/7, 39,200,0,0.05)   # yellow
hypoth_test_prop(1/7, 28,200,0,0.05)   # green
hypoth_test_prop(1/7, 30,200,0,0.05)   # blue
hypoth_test_prop(1/7, 30,200,0,0.05)   # red

#  Now do the test for all of the values as a 
#  goodness of fit test
source("../goodfit.R")
goodfit(c("Orange","Purple","Black","Yellow","Green","Blue","Red"),
        rep(1/7,7),
        c(29, 28, 16, 39, 28, 30, 30),
        0.05,
        FALSE)