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:

COLOR OBSERVED COUNT EXPECTED COUNT RESIDUAL

Brown 127

Red 38

Orange 54

Yellow 63

Green 32

Blue 29

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.)