Question

*Are candy color pieces uniformly distributed?*

In a 2 ounce bag of Skittles, there are green, red, yellow, orange and purple pieces. Ideally, each bag should have the same amount of pieces for each color (so colors/categories are equally likely.)

PROJECT: Pick (or Google a picture of) a bag of candy (Skittles,
M&Ms or Mike & Ikes, etc) that fulfills the requirements
listed below and perform a *goodness of fit test for uniform
distribution* (use a 0.05 significance level.)

Requirements

- The sample must contain at least 50 whole pieces
- Each sample must contain 4 to 7 categories (red, yellow, blue…)

Please include in your project:

- Title your project.

- Statement of claim: For example “My bag of skittles has 50 whole pieces: 12 blue, 18 red ... Using a 0.05 significance level I will test the claim that the candy colors are uniformly distributed.” In this statement you should mention the observed and expected values (hint if your expected values are fractions you may want to increase the sample size until you have whole numbers, n=50 is not divisible by 4 colors but n=52 is.)

- Test the claim with Goodness Of Fit Test using the same format
as the 11-1 lecture video: H
_{o}, H_{1}, test statistic X^{2}, p-value, Reject/Fail to Reject and state the conclusion.

- Be creative with presentation of your work (colors, pictures, etc.) especially if your project is handwritten or a printout

Answer #1

Claim: My bag of skittles has 50 whole pieces: 12 purple, 10 yellow, 13 green, 9 orange & 11 red.

The hypothesis being tested is:

H0: The candy colours are uniformly distributed

Ha: The candy colours are not uniformly distributed

observed | expected | O - E | (O - E)² / E |

12 | 11.000 | 1.000 | 0.091 |

10 | 11.000 | -1.000 | 0.091 |

13 | 11.000 | 2.000 | 0.364 |

9 | 11.000 | -2.000 | 0.364 |

11 | 11.000 | 0.000 | 0.000 |

55 | 55.000 | 0.000 | 0.909 |

.91 | chi-square | ||

4 | df | ||

.9233 | p-value |

The p-value is 0.9233.

Since the p-value (0.9233) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the candy colours are uniformly distributed.

Are candy color pieces uniformly distributed?
In a 2 ounce bag of Skittles, there are green, red, yellow,
orange and purple pieces. Ideally, each bag should have the same
amount of pieces for each color (so colors/categories are equally
likely.)
PROJECT: Pick (or Google a picture of) a bag of candy
(Skittles, M&Ms or Mike & Ikes, etc) that fulfills the
requirements listed below and perform a goodness of fit test for
uniform distribution (use a 0.05 significance level.)
Requirements...

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Red...

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candies in a bag, and you can "Taste the Rainbow" with their five
colors and flavors: green, lime; purple, grape; yellow, lemon;
orange, orange; and red, strawberry. Unlike some of the other
multicolored candies available, Skittles claims that their five
colors are equally likely. In an attempt to reject this claim, a
4-oz bag of Skittles was purchased and the colors counted. Does
this sample contradict Skittle's claim at the .05 level?
Red...

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candies in a bag, and you can "Taste the Rainbow" with their five
colors and flavors: green, lime; purple, grape; yellow, lemon;
orange, orange; and red, strawberry. Unlike some of the other
multicolored candies available, Skittles claims that their five
colors are equally likely. In an attempt to reject this claim, a
4-oz bag of Skittles was purchased and the colors counted. Does
this sample contradict Skittle's claim at the .05 level?
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