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.