Skittles Original Fruit bite-size candies are multicolored candies in a bag, and

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 18 15 28 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 <

Explanation / Answer

here we go for goodness of fit using chi-square test

chi-squre=sum((O-E)2/E) with k-1 df, here k=5

sinnce every color is equalily likely so expected value would be for each colour=total/5=103/5=20.6

all calculation is done in the following table

(a)here test statistic=6.9516

(b)p-value=chi-squre(6.9516,4)=0.1385 (using MS-Excel command=CHIDIST(x=6.9516,df=4)

critical value of chi-square at alpha=0.5 and df=4 is given by 9.4878

since the critical value is more than the test statistic so we accept the claim that the five colors are equally likely.(also p-value is more than the alpha)

observed(O) Expected(E) (O-E) (O-E)2/E red 26 20.6 5.4 1.415534 orange 18 20.6 -2.6 0.328155 yellow 15 20.6 -5.6 1.52233 green 28 20.6 7.4 2.658252 purple 16 20.6 -4.6 1.027184 total 103 103 -7.1E-15 6.951456

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