Question

MARS claims that Skittles candies should be comprised of 30% purple, 10% orange, and 20% should be red, yellow, and green. Business students count a large bag of Skittles and find 265 red, 279 purple, 303 yellow, 271 green, and 212 orange candies.

a. Set up the competing hypotheses to test if at least one proportion is different than the value claimed by MARS.

b. Calculate the value of the test statistic and determine the degrees of freedom.

c. Compute the p-value. Does the evidence suggest that at least one proportion is different from the claimed value at the 5% significance level?

Answer 1

Ans:

a)

H₀: The proportion of colors is same as claimed.

H_a:At least one proportion is different from the claimed value.

	Observed(fo)	pi	Expected(fe)	(fo-fe)^2/fe
Red	265	0.2	266	0.004
purple	279	0.3	399	36.090
yellow	303	0.2	266	5.147
green	271	0.2	266	0.094
orange	212	0.1	133	46.925
Total	1330	1	1330	88.259

b)Test statistic:

Chi square=88.259

df=5-1=4

c)p-value=CHIDIST(88.259,4)=0.0000

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to suggest that at least one proportion is different from the claimed value at the 5% significance level.