Judith S. Nuño AP Biology 12/1/2005
Title: ChiSquare Analysis and M&M’s
Purpose:
to practice using chisquare analysis
to compare the observed and expected color ratios of M&M’s candies
Null Hypothesis:
If the Mars Co. M &M sorters are doing their job correctly, then there should be no difference in M&M color ratios between actual storebought bags and what the Mars Co. claims are the actual ratios.
Materials: bags of M&M’s
Procedure:
1. Obtain bags of M&M’s
2. Determine the expected number of M&M’s (http://us.mms.com/us/about/products/ a. Record in Data Table A
3. Determine the actual number of M&M’s of each color a. Record in Data Table A
4. Calculate the ChiSquare value. a. Show your calculations!
5. Determine degrees of freedom (number of classes − 1) 6. Use the 0.05 probability level as the critical value.
a. If the calculated chisquare value is less than the 0.05 value, we accept the NULL hypothesis.
b. If the value is greater than the value, we reject the NULL hypothesis. 7. Repeat using a different type of M&M’s. Record in Data Table B
8. Share your data with classmates
Data Table A: Expected and Observed Color Ratios for M&Ms (type = __________) Expected* (percent)
Red Brown Blue Yellow Green Orange
**Observed (number/percent)
/ / / / / / /
Data Table B: Expected and Observed Color Ratios for M&Ms (type = __________) Expected* (percent)
Red Brown Blue Yellow Green Orange
**Observed (number/percent)
/ / / / / / /
*Source = http://us.mms.com/us/about/products/
** # M & M's of one color x 100
total # M & M's
c
2 (Observed Value Expected Value) 2
=
Judith S. Nuño AP Biology 12/1/2005
Data Table C:
Χ
2 Calculations Individual Data M&M’s Type _______________A B C D E
Obs Exp (Obs − Exp) (Obs − Exp) 2 Obs − Exp)
2
Exp Red
Brown Blue Yellow Green Orange
Χ
2Degrees of Freedom
Accept or reject null hypothesis?
*
Data Table D:
Χ
2 Calculations Individual Data M&M’s Type _______________A B C D E
Obs Exp (Obs − Exp) (Obs − Exp) 2 Obs − Exp)
2
Exp Red
Brown Blue Yellow Green Orange
Χ
2Degrees of Freedom
Accept or reject null hypothesis?
*
Χ
2 tutorial http://www.ndsu.nodak.edu/instruct/mcclean/plsc431/mendel/mendel4.htm Discussion and Analysis:Are the Mars Co M&M sorters doing a good job? Explain!
Conclusion: The null hypothesis, that the M&M sorters are doing a good job, is (accepted, rejected) for (type of M&Ms).
You will have a conclusion for each type of M&M examined!
Reflection: personal statement
*
If theΧ
2 is smaller than the critical value for the indicated degrees of freedom, then we accept the null hypothesis that the variation in color percentages is due to chance (random) variation.If the
Χ
2 is larger than the critical value for the indicated degrees of freedom (# classes1), then we reject the null hypothesis and conclude that the sorters are doing a statistically significant poor job.The test does NOT indicate reasons for a poor job!
Probability Degrees of
Freedom 0.9 0.5 0.1 0.05 0.01 1 0.02 0.46 2.71 3.84 6.64 2 0.21 1.39 4.61 5.99 9.21 3 0.58 2.37 6.25 7.82 11.35 4 1.06 3.36 7.78 9.49 13.28 5 1.61 4.35 9.24 11.07 15.09
M&M's.com > About M&M'S® Brand > Products
There's more to M&M'S® Chocolate Candies than delicious chocolate and colorful candy coatings! Get fun facts and nutritional info about your favorite M&M'S® Chocolate Candies.
An American original—the first ever M&M'S®
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Delicious, creamy ice cream that'll keep you cool.
Choose colors, messages, and more!
Where to Buy M&M'S® Candies | Change Your Email | Contact Us | Site Map | International
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Get the lowdown on the candy that started it all— original M&M'S® Milk Chocolate Candies.
M&M'S® Milk Chocolate Candies were first manufactured in 1940, when Forrest E. Mars, Sr. formed the company in Newark, New Jersey. His original idea was to offer
chocolates with a sugar shell that could be sold throughout the year and wouldn't melt during the summer.
Amount/Serving %DV**
Calories 240
Fat Calories 90 Total Fat 10g 15% Saturated Fat 6g 30%
Trans Fat 0g
Cholesterol 5mg 2%
Sodium 30mg 1%
Total Carb. 34g 11%
Fiber 1g 4%
Sugar 31g
Protein 2g
Vitamin A*
Vitamin C*
Calcium 4%
Iron 2%
Riboflavin 4%
Niacin
Thiamine
Serving Size 1.69 ounces (47.9grams)
*Contains less than 2 percent of the Daily Value of these nutrients. **Percent Daily Values (DV) are based on a 2,000 calorie diet. Available in these sizes: 1.69 oz., 3.14 oz., 5.3 oz., 9.4 oz., 14 oz., 21.3 oz., 52 oz.
M&M's.com > About M&M'S® Brand > Products > Milkchocolate
Mendelian Genetics
Mendel's First Law
Variations to
Mendel's First Law
Pedigree Analysis
Mendel's Second
Law
Chi-Square Test
Pleiotropy
Epistasis
Modifier Genes
Penetrance and
Expressivity
Study Questions
Mendelian Genetics
Overheads
Mendelian Genetics
WWW Links
Genetic Topics
The Chi-Square Test
An important question to answer in any genetic experiment is how
can we decide if our data fits any of the Mendelian ratios we have
discussed. A statistical test that can test out ratios is the
Chi-Square or Goodness of Fit test.
Chi-Square Formula
Degrees of freedom (df)
= n-1 where n is the number of classes
Let's test the following data to determine if it fits a 9:3:3:1 ratio.
Observed Values
Expected Values
315 Round, Yellow Seed
(9/16)(556) = 312.75 Round, Yellow
Seed
108 Round, Green Seed
(3/16)(556) = 104.25 Round, Green
Seed
101 Wrinkled, Yellow
Seed
(3/16)(556) = 104.25 Wrinkled,
Yellow
32 Wrinkled, Green
(1/16)(556) = 34.75 Wrinkled,
Green
556 Total Seeds
556.00 Total Seeds
Number of classes
(n) = 4
Mendelian Genetics
