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: My bag has 50 pieces. It has 6 green, 15 red, 9 purple, 12 yellow and 8 orange. 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: Ho, H1, test statistic X2, 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

The hypothesis being tested is:

H₀: The candy colors are uniformly distributed

H_a: The candy colors are not uniformly distributed

observed	expected	O - E	(O - E)² / E
6	10.000	-4.000	1.600
15	10.000	5.000	2.500
9	10.000	-1.000	0.100
12	10.000	2.000	0.400
8	10.000	-2.000	0.400
50	50.000	0.000	5.000
5.00	chi-square
4	df
.2873	p-value

The chi-square test statistic is 5.00.

The p-value is 0.2873.

Since the p-value (0.2873) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we have insufficient evidence to conclude that the candy colors are uniformly distributed.