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
16	24	25	30	27

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


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

Answer 1

Solution:

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.

We have to test if this sample contradict Skittle's claim at the 0.05 level of significance.

Thus hypothesis of the study are:

H0: Multicolored candies in a bag of five colors are equally likely

Vs

H1:Multicolored candies in a bag of five colors are not equally likely

Part a) Find the test statistic.

Since we have to test if observed data fits well to the expected frequencies, we use Chi-square goodness of fit test.

Where

Oi = Observed frequencies

Ei = Expected Frequencies = N / k = 122 / 5 = 24.4

Color	Oi	Calculations	Ei	Oi^2/Ei
Red	16	=122/5	24.4	10.49
Orange	24	=122/5	24.4	23.61
Yellow	25	=122/5	24.4	25.61
Green	30	=122/5	24.4	36.89
Purple	27	=122/5	24.4	29.88
	N = 122

Part b) Find the p-value. (Give your answer bounds exactly.)

df = k   - 1 = 5 - 1 = 4

Look in Chi-square table for df = 4 row and find the interval in which fall and then find corresponding right tail area interval.

Chi-square test statistic value = fall between 1.064 and 7.779

and its corresponding right tail area is between 0.900 and 0.100

That is: between 0.100 and 0.900

Thus p-value range is:

0.100 < p < 0.900

Since P-value > 0.100 level of significance, we fail to reject H0.

thus we conclude that: Skittles claim is true that: the other multicolored candies available, that their five colors are equally likely.

Thus sample data does not contradict Skittle's claim at the .05 level of significance.