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.

What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)? (2 points total, 1 for each answer)

State the null and alternative hypotheses in words (2 points total: 1 for each hypothesis)

Calculate X2 statistic (3 points total: 1 for final answer, 1 for setting up the correct OFs and EFs, 1 for correct calculation process)

Calculate the degree of freedom and then identify the critical value (2 points total, 1 for df, 1 for critical value)

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 (1 point total, .5 for each answer)

Explain the conclusion in a sentence or two (1 point)

Explanation / Answer

variable in this test -- frequency of  ice cream flavors.

type of variable --- nominal

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

alternate hypothesis:three flavors are not equally popular

from abvoe data:

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

critical value at 0.05 significance level and 2 degree of freedom =5.991

as test stat is lower then critical value we fail to reject the hypothesis

we have insufficient evidence to conclude that three flavors are not equally popular.

observed Expected Chi square Type Probability OF EF=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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