Calculation of Chi Square by Hand

Hand Calculation of M&M Chi-square Goodness of Fit Example

ASCI 662, Module 9, Activity 9.3

Problem Sheet

This exercise will replicate the classic M&M Chi-Square Goodness of Fit Example often used in statistic

classes. Follow the instructions below and calculate your own M&M Chi-Square Goodness of Fit. First,

collect your data independently and run the calculations by hand. Then, perform the same test using

SPSS and see if you come out with the same results.

Instructions:

1. The published typical percentage of M&Ms in a bag of M&Ms is listed below. Buy a bag of

M&Ms and count the total number of M&Ms in that bag. Then figure out the number of each

color of M&Ms that should be in that bag according to the published typical percentage of

M&Ms (Expected). Once you figure out your expected frequency of M&Ms, count the number

of each color M&M ) Observed) and record that number in your table below.

Total number of M&Ms

M&M Expected and Actual Distribution by Color:

Color/% Observed Expected Diff (Obs-Exp) Diff 2 (Obs-

Exp)2/Expected

Blue 24%

Orange 20%

Green 16%

Yellow 14%

Red 13%

Brown 13%

∑ [(Obs-Exp)2/Expected] =

X2 calculated = ∑ [(Obs-Exp)2/Expected] =

2. Look up X2 in Table C-7 (Critical Values of Chi-Square) based on alpha level = .05 and calculated

degrees of freedom (df).

Df = number of categories – 1

X2 critical =

3. Stating your hypotheses and determining your results:

H0 (null hypothesis): The distribution of M&Ms is the same as the distribution stated by the M&M

company.

H1 (alternative hypothesis): The distribution of M&Ms is not the same as the distribution stated by the

M&M company.

If X2 calculated is greater than X2 critical, then we reject the null hypothesis Is

X2 calculated greater than X2 critical?

If “yes”, then we reject the null hypothesis.

If “no” then we accept the null hypothesis.

4. What are your results? Write your results in the box below.

Save this worksheet and name it “9.3 Hand Calculated MM exercise” as your deliverable for this

exercise.