Transcript Are Skittles colors evenly distributed
BY: Kristin Taylor
Introduction & Research Question
Question- Are the flavors in a 2.17 oz. bag of original Skittles evenly distributed?
Population of interest- 5 bags of 2.17 ounce original Skittles
Procedure
1.
2.
3.
4.
5.
6.
Pour one bag of Skittles onto a paper towel Sort the Skittles by color Count the # of each color and record Calculate total # of Skittles in individual bag Place skittles in a cup/bowl Repeat steps 1-5 for the remaining 4 bags
Intro & Research (cont.)
Weakness
The population size could have been larger The number of each color of Skittles could have been miscalculated, which would have skewed the sum in the bag
Strength
The experiment setup The Skittles were all the same size No half pieces
Data Collection
Data collected by: 1.
Sorting the colors in a 2.17 oz. bag of Original Skittles 2.
3.
Counting them & recording the total of each color Add up all the totals to get the total amount of Skittles in the bag 4.
Then divide the # of each color by the total # of Skittles to get the percentage EX. 11/58 = .189 ≈ 19%
I am confident that my sample represents the population because the total number of Skittles within the five bags were around the same total. The total ranged from 58-61. Therefore, I am confident that if a larger sample size was used then the total amount of Skittles would be within this range. Using the z-interval test on a TI-83, I’m 90% confident that the total amount of Skittles in a 2.17 0z. bag would range from 55-65 Skittles.
BAG ONE
6 4 2 0 14 12 10 8
Total # of each Color Color
GREEN PURPLE YELLOW RED ORANGE
Count
11 13 13 9 12
%
19 22 22 16 21
BAG TWO
16 14 12 10 8 6 4 2 0
Total # of each Color
Green Red Purple Orange Yellow
Color
GREEN PURPLE YELLOW RED ORANGE
Count
14 14 13 11 9
%
23 23 21 18 15
BAG THREE Color
GREEN PURPLE YELLOW RED ORANGE
Count
11 16 10 12 10
%
19 27 17 20 17 6 4 2 0 18 16 14 12 10 8
Total # of each Color
BAG FOUR Total # of each Color
6 4 2 0 18 16 14 12 10 8
Color
GREEN PURPLE YELLOW RED ORANGE
Count
12 10 11 17 11
%
20 16 18 28 18
BAG FIVE
20 18 16 14 12 10 8 6 4 2 0
Total # of each Color Color
GREEN PURPLE YELLOW RED ORANGE
Count
18 14 4 13 11
%
30 23 6.7
22 18.3
Cumulative Average
Color
GREEN PURPLE YELLOW RED ORANGE
Count
66 67 51 62 53 The graph to the right shows the sum of each color within the sample population 5-number summary: Min- 51 Q1- 52 Mean: 59.8
σ: 6.62
Med- 62 Q3- 66.5
Max- 67
Color Total
80 60 40 20 0 Green Red Purple Orange Yellow Shape: the graph is roughly symmetric Outliers: there are no outliers Center: 62 Spread:51- 67
Inference Procedure
Null Hypothesis- The flavors of Original Skittles in a 2.17 oz. bag are evenly distributed. Alternative Hypothesis- The flavors of Original Skittles in a 2.17 oz. bag are not evenly distributed.
Significance level: α =.05
Sample size: 5 bags of 2.17 oz. Skittles
Chi-square Test
Ho: The flavors of Original Skittles in a 2.17 oz. bag are evenly distributed.
Ha: The color of Original Skittles in a 2.17 oz. bag are not evenly distributed.
Class
Green Purple Yellow Red Orange
Observed
66 67 51 62 53
Expected
59.8
59.8
59.8
59.8
59.8
Step 2: The χ² GOF Test will be used Check Conditions: 1.
2.
The data does not come from a SRS therefore, I may not be able to generalize about the population The expected numbers are greater than 5 Step 3: Χ ² = ∑(O-E)² E = (66-59.8)² + (67-59.8)² + (51-59.8)² + (62-59.8)² + (53-59.8)² 59.8 59.8 59.8 59.8 59.8
= 3.66
Step 4: Using a TI-84, the p-value was 0.45
There is strong evidence to reject the null hypothesis at the α = .05 level because the p-value is greater than .05 (.45 ≥ .05). Therefore, the flavors in a 2.17 oz. bag of Original Skittles are not evenly distributed, which can be seen in the graphical displays of each individual bag. From reviewing my graphical displays and charts I noticed that within four of the bags of Skittles only two of the colors within the bag had equal amounts.