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:

1. Title your project.

2. 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.)

3. Test the claim with Goodness Of Fit Test using the same format as the 11-1 lecture video: H_o, H₁, test statistic X², p-value, Reject/Fail to Reject and state the conclusion.

4. 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.