It has long been debated what the color distribution is in a bag of m&m's. Research results from the internet show a range of color proportion for a bag of plain m&m's. The m&m Mars Company no longer publishes "official" information regarding this topic. However the curiosity of people perpetuates this information as a popular research topic.
Use the following Tables to summarize the data:
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Orange
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Yellow
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Red
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Brown
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Green
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Blue
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Total
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% Observed
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100%
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% Expected
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20
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14
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13
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13
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16
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24
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100%
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# Observed
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#Expected
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Difference
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Total Class Bags (Unequal Proportions)
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Orange
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Yellow
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Red
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Brown
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Green
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Blue
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Total
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% Observed
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100%
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% Expected
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20
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14
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13
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13
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16
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24
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100%
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# Observed
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#Expected
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Difference
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Your Bag (Equal Proportions)
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Orange
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Yellow
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Red
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Brown
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Green
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Blue
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Total
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% Observed
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100%
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% Expected
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16.67
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16.67
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16.67
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16.67
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16.67
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16.67
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100%
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# Observed
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#Expected
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Difference
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Total Class Bags (Equal Proportions)
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Orange
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Yellow
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Red
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Brown
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Green
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Blue
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Total
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% Observed
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100%
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% Expected
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16.67
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16.67
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16.67
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16.67
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16.67
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16.67
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100%
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# Observed
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#Expected
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Difference
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Instructions:
Step 1: Open your bag of m&m's and sort the candy by color. Count the number of m&m's of each color and record the number according to the corresponding color in the "Your Bag" tables in the #Observed row.
Step 2:Record your #Observed, by color on the class data table at the front of the class. (In class students only) ***
Step 3: Record the total class counts on your data sheet in the "Total Class Bags tables. In the #Observed row.
Step 4:Calculate the %Observed row numbers as (Color#/Total# in Bag) x 100 for all tables.
Step 5: Calculate the #Expected row numbers as Total # in bag x (%Expected/100)for all tables.
Step 6: Calculate the Difference as (#Observed - #Expected)for all tables.
On-Line Students will get this information after Monday's in-class session. You will use the class information provided following the Monday class to fill in the "Total Class Bags"tables above.
Using the appropriate data in the tables above, run the following:
Test 1 = Using your bag of m&m's, calculate a Chi-square Goodness of Fit assuming that the proportion of the observed colors of m&m's will be the sameas an unequal predetermined proportion of colors as determined by the m&m Mars Company statistics.
Test 2 = Using your bag of m&m's, calculate a Chi-square Goodness of Fit assuming that the proportion of the observed colors of m&m's will observed values will be the same as an equal predetermined proportion of colors.
Test 3 = Using the Total Class data, calculate a Chi-Square Goodness of Fit assuming that the proportion of the observed colors of m&m's will observed values will be the same as an unequal predetermined proportion of colors as determined by the m&m Mars Company statistics.
Test 4 = Select one color of m&m's from your bag. Using the Chi-square test of Association, determine whether that one color is similar to the distribution of the same color in the total class data.
Answer the following questions for each of the 4 tests. (You will answer these same questions 4 times)
1. State the research scenario.
a. Look at research scenario examples from various lectures and write your own for each test.
2. State the Null Hypothesis - Write this in the proper form for the test you will run.
3. State the Research Hypothesis - Write this in the proper form for the test you will run.
4. State the statistical analysis method that you ran
5. Copy the output tables to your HW document.
6. Explain the meaning of the information from each table and/or graph.
7. Provide a COMPLETE write-up for the research scenario and test.
Chi Square/m&m information for HW
The numbers for the class have been tallied. The numbers are as follows:
Total class bags counts for :
Orange = 257, Yellow = 118, Red = 144, Brown = 95, Green = 199, Blue = 84 Total m&m's in bags = 897
Enter this data into the tables for "Class Bags", Observed counts.
You will use this information for any analysis using "Class Bags".
To get the information for "Your Bag" you must purchase a single bag of Plain m&m's. It must weigh 1.69 oz.
Before eating the m&m's you must count the m&m's of each color and record the color counts in your HW assignment. This will be the Observed count for the "My Bag" tables. You can obtain the expected color counts and percentages from the SPSS printout for each test.
You will need to create your data sets for each type of analysis in SPSS.
Look carefully at Test #4. Please contact me if you have problems with this.