The Candy Man Can
AP Stats 11.1
You will be able to provide one or more of these skills for your group today
Design Two-way Tables
chi-Square Test
M&Ms Data Collection
Organization
Recognizing Similarities
Learning Tests on Nspire
Stick-with-it-ness
MINC or State Plan Do Conclude
Degrees of Freedom
Quantitative vs Categorical
Roles
Captain – Check to make sure group members are all getting the same solutions, Keep group together
at all times, Encourage contributions from quieter group members
RM - Team Questions, Make sure everyone has supplies, Organize clean up, Read task card
RR - Make sure everyone completes notes, Make sure all group members complete all calculator work,
Add your group’s calculations to the front board (X2 , p-value and conclusion)
Facilitator – QS, Watch the time for completion, Keep the group moving, Make sure everyone has
notes ready to show the instructor
The Candy Man Can
AP Stats 11.1
Supplies:
Each person needs an Nspire calculator, Pencil, and Notebook.
Small bag of M&M’s® Milk Chocolate Candies for each pair of students.
Mars, Incorporated, which is headquartered in McLean, Virginia, makes milk chocolate candies. Here’s
what the company’s Consumer Affairs Department says about the color distribution of its M&M’S Milk
Chocolate Candies:
On average, the new mix of colors of M&M’S Milk Chocolate Candies will contain 13 percent of each of browns and reds, 14 percent
yellows, 16 percent greens, 20 percent oranges and 24 percent blues.
The purpose of this Activity is to compare the color distribution of M&M’S in your individual bag with the advertised distribution. We
want to see if there is enough evidence to dispute the company’s claim. For the time being, assume that your bag is a random sample
of M&M’S Milk Chocolate Candies from the population of candies produced in a particular batch.
Task 1:
1) Open your bag and carefully count the number
of whole M&M’S of each color as well as the
total number of M&M’S in the bag.
Make a table on your paper like the one
shown. In the “Observed” column, fill in the
counts, by color, and the total number of
M&M’S in your bag. Leave the other columns
blank for now.
2) Assuming that the company’s claim is true, how many of each color would you expect in your bag? For example, suppose
that your bag has 60 M&M’S. How many blue M&M’S should you expect? If 24% of all M&M’S Milk Chocolate Candies are
blue, then you’d expect (0.24)(60) = 14.40 blue M&M’S, on average, in a bag with 60 M&M’S. In a similar way, you can
calculate the expected counts for the other five colors.
Compute the expected counts (to two decimal places) for your bag; record your results in the “Expected” column of your
table. Check that the sum of the expected counts is equal to the number of M&M’S in your bag.
The Candy Man Can
AP Stats 11.1
3) How close are your observed counts to the expected counts? To answer this question, calculate the difference for each
color: Observed − Expected. Record these differences in the appropriate column. Find the sum of the values in this
column. What do you notice about ∑(Observed − Expected)?
In Step 3, the sum of the difference values should be 0 (up to roundoff error). Does that mean your individual bag matches
the color distribution claimed by Mars, Inc., perfectly? Of course not. You get a total difference of 0 because the positive and
negative values cancel each other. How can we fix this problem? We could use absolute values, but instead, we choose to
square the difference values (does this remind you of anything earlier in the text?).
4) Compute the values of (Observed − Expected)2 and fill in the next column of your table. Find the sum of the values in this
column. Compare your results with those of your classmates.
5) In the last column of your table, divide the values in the (Observed − Expected)2 column by the corresponding expected
counts, then find the sum. This final result is called the chi-square statistic and is denoted byχ2 (the lowercase Greek letter
chi, pronounced “kye”). Keep this number handy—you will use it later in the chapter.
6) If your sample reflects the distribution advertised by Mars, Inc., there should be very little difference between the observed
counts and the expected counts. Therefore, the calculated values making up the sum χ2should be very small. Are the entries
in the last row all about the same, or do any values stand out because they are much larger than the others? Did you get
way more or way fewer of a particular color than you expected?
7) Compare your value of χ2 with the results obtained by your classmates. How do we know if a particular χ2 statistic is large
enough to provide convincing evidence against the company’s claim? We need to learn more about the distribution of the chisquare statistic before we can answer this question.
8) RR: Record your χ2 value on the front board.
Task 2:
1) Everyone in the group needs to create a graph that represents your data on
the Nspire.
2) Enter three columns: color, expected and observed. To make the graph ,
highlight all 3 columns, then press menu, data, summary plot, change
display to New Page then enter.
3) Make a 4th column in your spreadsheet and use the χ2 formula in the
equation cell to calculate χ2 with your calculator.
The Candy Man Can
AP Stats 11.1
Task 3:
As a class go through slides 1-20 on the 11.1 power point. During the slides make notes and write up a sample chi-square test
for your data. Use State, Plan, Do, Conclude or MINC to organize your notes.
C
N
Include description
of H0 and Ha,
significance level, 𝛼
Name of test
and conditions
M
I
Find χ2 and
the p-value
Interpret your results
Final Product:
Your 11.1 notes which should
include a complete sample of a chisquare test.
State: Include description of H0 and Ha,
significance level, 𝛼
Plan: Name of test and conditions
Do: Find χ2 and the p-value
Conclude: Interpret your results