A marketing research firm wishes to study the relationship between wine consumpt

Question

A marketing research firm wishes to study the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:

(a) For each row and column total, calculate the corresponding row or column percentage.

  
(b) For each cell, calculate the corresponding cell, row, and column percentages. (Round your answers to the nearest whole number.)

(c) Test the hypothesis that whether people drink wine is independent of whether people watch tennis. Set = .05. (Round your answer to 3 decimal places.)

(Click to select)RejectDo not reject H0. Conclude that whether a person drinks wine and whether a person watches tennis are (Click to select)DependentIndependent events.

Watch
Tennis Do Not
Watch Tennis Totals Drink Wine 5 50 55 Do Not Drink Wine 15 30 45 Totals 20 80 100

Explanation / Answer

a)

b)

c)H0 : the two classifications are statistically independent versus
Ha : the two classifications are statistically dependent

First we have to calculate the expected value of the two nominal variables.

Expected frequencies. Er,c = (nr * nc) / n, where
Er,c is the expected frequency count for level r of Variable A and level c of Variable B, nris the total number of sample observations at level r of Variable A, nc is the total number of sample observations at level c of Variable B, and n is the total sample size

Degrees of freedom. The degrees of freedom (DF) is equal to:

DF = (r - 1) * (c - 1) = (2-1)*(2-1) = 1

Test statistic. The test statistic is a chi-square random variable (2) defined by the following equation.

2 = [ (Or,c - Er,c)2 / Er,c ]

2 = [(5-11)2/11] + [(50-44)2/44] + [(15-9)2/9] + [(30-36)2/36] = 100/11 = 9.091

At = .05, 2crit= 3.841

As 2 > 2crit, Reject H0, A person drinks wine and a person watches tennis are Dependent events

Row 1 40% Row 2 60% Column 1 20% Column 2 80%

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