Ryan Scott
Assignment: Excel Spread Sheet
Grade Range: High School
Subject Area: AP Biology
Topic: Chi-Sqaure Analysis
Standards:
Curriculum: Tied to AP Lab #7
ISTE Standards: 1c, 3d, 4c
M&M Statistics/A Chi Square Analysis
Description:
The purpose of this assignment is to give students an experience with using Chi-Square analysis.
The purpose of a chi square is to determine if a prediction can be confirmed, or are different based on chance or if they are actually different. In this activity, AP biology students will be trying to determine if the number of M&M’s in an individual bag is actually what M&M’s claims that it is. After this activity is complete, students will be using a Chi-Square during AP Lab #7. A follow up problem has been given to see if the students are able to complete a chi-square correctly.
Steps of lessons:
Expected % of M&M’s in Each Bag
Brown
Yellow
13%
14%
12%
15%
Red
Green
13%
16%
12%
15%
Blue
Orange
24%
20%
23%
23%
To test this hypothesis we will need to calculate the X 2 statistic, which is calculated in the following way:
X 2 = Σ(sum of) (O-E) 2
E
Where :
-O is the observed (actual count)
-E is the expected number for each color category.
In other words:
X 2 = Σ(sum of) (Observed Value- Expected Value) 2
(Expected Value)
The main thing to note about this formula is that, when all else is equal, the value of X 2 increases as the difference between the observed and expected values increase.
On to it!
1.
Open a bad of M&M’s and split them up between members of your lab group and place them on your paper plate.
2.
DO NOT EAT ANY OF THE M&M’S (for now!)

3.
Determine the expected number of M&M’s for your bag by counting the total number of
M&M’s in the bag and multiplying it by the percentage on the table above. Record this in the excel column labeled expected.
4.
Separate the M&M’s into color categories and count the number of each color of M&M you have. Record this into excel columns labeled observed.
5.
Now create a column that is labeled (o-e). This is for your observed-expected value. Subtract your observed row from your expected row in excel.
6.
Next, you will need to create a column labeled (o-e) 2 . This column should be used to square the value found in the previous column (o-e).
7.
Finally, you will need to divide the column (o-e) 2 by the expected value e. This will give a value.
Add all of the colors values in this column together.
8.
Determine the degrees of freedom (number of color categories -1)
9.
Use the probability table and use a .05 probability level as the critical value. Read the parameters for using the table and decide between the two options below.

If the calculated chi-square value is greater than the .05 value, we reject the NULL hypothesis

If the value is less than the .05 value, we accept the NULL hypothesis
10.
Once completed, answer the questions that follow, and complete the chi-square example.
Accept the null hypothesis Reject
Degrees of
Freedom
1
2
3
4
5
Probability
0.05
3.84
5.99
7.82
9.49
11.07
0.01
6.64
9.21
11.35
13.28
15.09
Follow-Up:
1.
Based on your individual sample, should you accept or reject the null hypothesis? Why?
2.
If you rejected your null hypothesis, what might be some explanations for your outcome?
Complete the following Chi-Square:
A
Observed (o)
B
Expected (e)
C
(o-e)
D
(o-e) 2
Green 72 63
Albino 12 21
Sum (Σ) of (o-e) 2 = X 2 e
E
(o-e) 2 e

Degrees of Freedom
Accept or Reject NULL hypothesis?
(Use Probability Table)
Student Rubric
Task
Chi-Square Completed
Accurately determined to accept or reject hypothesis
Explanation of accepting or rejecting hypothesis
Practice problem completed correctly
Total
Student Example:
Points Possible
10
5
5
10
30
Points Earned