Question

7.13 Favorite Skittles Flavor Skittles are a popu- lar fruity candy with five different flavors (colored green, orange, purple, red, and yellow). A sample of 66 people recorded their favorite flavor and the results are shown in Table 7.8. Perform a chi-square test, as indicated in the steps below, to see whether or not the flavors are equally popular. . (a) State the null and alternative hypotheses. (b) If every flavor of skittle were equally popular, how many people (in a sample of 66) would we expect to choose each? (c) How many degrees of freedom do we have? (d) Calculate the chi-square test statistic. (e) What is the conclusion about the popularity of the skittles flavors? Table 7.8 Skittles popularity Green Orange Purple 189 15 Red 13 Yellow 11

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Answer 1

Answer a)

The following null and alternative hypotheses need to be tested:

H0​: p1​=0.20,p2​=0.20,p3​=0.20,p4​=0.20,p5​=0.20

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

Answer b)

If every flavor were equally population

We would expect = 66*0.20 = 13.2 people to choose each

Answer c)

The number of degrees of freedom is df = No. of flavors - 1 = 5 - 1 = 4

Answer d)

The following table is obtained: Categories Observed Expected 66*0.20=13.2 Green Orange 66*0.20=13.2 (fo-fe)2/fe (18-13.2)2/13.2 = 1.745 (9-13.2)2/13.2 = 1.336 (15-13.2)2/13.2 = 0.245 (13-13.2)2/13.2 = 0.003 (11-13.2)2/13.2 = 0.367 Purple 66*0.20=13.2 Red 66*0.20=13.2 Yellow 66*0.20=13.2 Sum = 3.697

The Chi-Squared statistic is computed as follows: (0; - E:) _ L = 1.745 +1.336 +0.245 +0.003 +0.367 = 3.697 E 4

Answer e)

Rejection Region

Based on the information provided, the significance level is a = 0.05, the number of degrees of freedom is df = 5-1 = 4, so then the rejection region for this test is R = {x?:x >9.488

= 9.488, it is then concluded that the null hypothesis is Since it is observed that x = 3.697x not rejected.

Therefore, there is NOT enough evidence to the claim that the flavors are not equally popular.

In other words, 0.05 significance level, it can be claimed that all Skittles flavor are equally popular.