Informal Solution to: LAB ACTIVITY 1
Let's do a fun
(albeit slightly silly) goodness-of-fit test, possibly
including partitioning. You are to test the null hypothesis that all
six
colors of M&Ms are represented equally in a large batch. You
have suffered
long and hard (with stained fingertips, and being forced to
ingest many
calories) to gather the following data about the color distribution.
If
you reject your null hypothesis at the 0.05 level of
significance, use
partitioning to show why.
Here's the data that
you have:
Ei = 343/6 = 57.167
COLOR OBSERVED COUNT EXPECTED COUNT RESIDUAL
Brown 127 57.167 69.833
Red 38 57.167 -19.167
Orange 54 57.167 -3.167
Yellow 63 57.167 5.833
Green 32 57.167 -25.167
Blue 29 57.167 -28.167
Total 343
Be sure to write down
both your null and alternative hypotheses and list
your assumptions! What do you conclude?
(Later on, if you
partition as in Topic 4, show that the "sub-test" X^2obs
add up to (approximately) that of the original test statistic
and that the
degrees of freedom also add up properly.)
H0: The color of
M&M’s candies follow a uniform distribution
Ha: The color of
M&M’s candies follow some other distribution
Samples are independent and random, there are no
expected counts less than 1 or 5 and the data are categorical
Critical Value: = 11.070
Test statistic = sum(residual2/expected)
= 117.46
117.46>11.070, reject H0: the color
of M&M’s candies does not follow a uniform distribution.
Partitioning to follow.