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Chi Square Test of Variance

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Question 1
A bar owner is interested in customer preference for three (3) different brands of beer: Molson's, Corona, and Guinness. One hundred twenty customers are randomly selected and are asked to taste each beer and indicate their preference. The population from which the customers were drawn showed no particular preference for each of the three different brands of beers.
a. What are the expected cell frequencies for each of the three brands?
b. State the Null hypothesis.
c. After the 120 customers indicate their preference for one of the three brands, the bar owner finds:
a. 30 customers preferred Molson's
b. 50 customers preferred Corona, and
c. 40 customers preferred Guinness
At the (α= 0.5 level of significance), what should the bar owner conclude?
d. If the bar owner used a more stringent criterion to test the null hypothesis (α= .01 level of significance), what should the bar owner's conclusions be?

Question 2
The same bar owner has been quite absorbed by her interests in beer preferences. This time she randomly selects 150 men and 100 women to taste the same three different brands of beer and to declare his or her preference. Below is the resulting data:
Molson's Corona Guinness Totals
Men 55 35 60 150
Women 35 45 20 100
Totals 90 80 80 250

a. If gender makes no difference to beer preferences, what are the expected cell frequencies?
b. State the null hypothesis.
c. What can the bar owner conclude about the relationship between gender and beer preferences? (α= .05)

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Solution Summary

The solution provides step-by-step method of performing chi-square test of variance for both independent and dependent samples. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, tabulation of observed frequencies, calculation of expected frequencies, calculation of chi-square, calculation of degrees of freedom, decision rule and interpretation of results) have been explained in details.

Solution provided by:
Anwesha Ghosh, MSc
Education
  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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