Two employees at an ice cream store were discussing the popularity of the three

Question

Two employees at an ice cream store were discussing the popularity of the three basic ice cream flavors: Vanilla, Chocolate, and Strawberry. Employee A thought that the three flavors are equally popular but employee B didn’t think so. To settle their debate, they decided to tally the number of customers asking for those flavors for a whole day. There were 30 customers asking for one of those flavors that day: 13 asked for vanilla, 8 asked for chocolate, and 9 asked for strawberry. A Chi-Square Test for Goodness of Fit using a = .05 as the significance level.

a) Calculate X2 statistic (PLEASE show work with the OFs and EFs- thank you)

b) Calculate the degree of freedom and then identify the critical value

c) Compare the X2 statistic with the critical value, then report the hypothesis test result, using “reject” or “fail to reject” the null hypothesis in the answer

d) Explain the conclusion in a sentence or two

Explanation / Answer

here null hypothesis: three flavors are equally popular . p1=p2=p3 =1/3

alternate hypothesis: all flavours are not equall popular.

applying chi square goodness of fit test:

a) from above X2 statistic =1.40

b) degree of freedom =number of categories -1 =3-1 =2

c) for 2 degree of freedom and 0.05 level ; critical value =5.991

as test stat is lower then critical value ; fail to reject” the null hypothesis

d) we do not have sufficient evidence at 0.05 level that three flavors are differently popular,

(please revert if you want any clarification regarding calculations)

observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E Vanilla 1/3 13.000 10.00 0.90 Chocolate 1/3 8.000 10.00 0.40 strawberry 1/3 9.000 10.00 0.10 1 30 30 1.4000

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