Question

Suppose someone claims he has the secret distribution for the colors of Skittles. You take a random sample of Skittles and wish to perform a hypothesis test to see if the data are consistent with this claim.

Color	Distribution Claim	Observed From Sample
Brown	.30	131
Yellow	.25	118
Red	.15	99
Orange	.10	52
Green	.12	49
Blue	.08	36

a. Construct the table of expected frequencies.

b. Calculate the appropriate χ2 statistic and degrees of freedom.

c. Estimate a p value using the attached table. Is this sample consistent with the claimed distribution?

Answer 1

Ans:

a)

Color	Distribution Claim	Observed(fo)	Expected(fe)	(fo-fe)^2/fe
Brown	0.3	131	145.5	1.45
Yellow	0.25	118	121.25	0.09
Red	0.15	99	72.75	9.47
Orange	0.1	52	48.5	0.25
Green	0.12	49	58.2	1.45
Blue	0.08	36	38.8	0.20
Total	1	485	485	12.91

b)Test statistic:

Chi square=12.91

df=6-1=5

c)p-value=CHIDIST(12.91,5)=0.0242

As,p-value<0.05,we reject the null hypothesis and we can conclude that sample data is not consistent with the claimed distribution.