Question

Skittles Original Fruit bite-size candies are multicolored 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	Orange	Yellow	Green	Purple
26	29	21	29	16

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
_____< p <_____

Answer 1

Claim: Five colors are equally likely.

The null and alternative hypothesis is

H0: P1 = P2 = P3 = P4 =P5

H1: At least one of the proportion is not equal.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*p

n = 121

p = 1 / 5

O	E	(O-E)	(O-E)^2	(O-E)^2/E
26	24.2	1.8	3.24	0.133884
29	24.2	4.8	23.04	0.952066
21	24.2	-3.2	10.24	0.42314
29	24.2	4.8	23.04	0.952066
16	24.2	-8.2	67.24	2.778512
			Total	5.24

a)

Degrees of freedom = Number of E's - 1 = 5 - 1 = 4

ii)

0.10 < P-value < 0.90

P-value > 0.05 we fail to reject null hypothesis.

Conclusion:

Five colors are equally likely.