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A marketing research firm wishes to study the relationship between wine consumption and whether a person...

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Statistics

A marketing research firm wishes to study the relationshipbetween wine consumption and whether a person likes to watchprofessional tennis on television. One hundred randomly selectedpeople are asked whether they drink wine and whether they watchtennis. The following results are obtained:

Watch
Tennis		Do Not
Watch Tennis		Totals
Drink Wine84250
Do Not Drink Wine123850
Totals2080100

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

Row 1%
Row 2%
Column 1%
Column 2%

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

Watch
Tennis		Do Not
Watch Tennis
Drink WineCell= %Cell= %
Row= %Row= %
Column= %Column= %
Do Not Drink WineCell= %Cell= %
Row= %Row= %
Column= %Column= %

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

χ2χ2 =         

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

Answer & Explanation Solved by verified expert
4.1 Ratings (563 Votes)

a)

dividing row and column total with grand total
Row 1 50.00%
Row 2 50.00%
Column 1 20.00%
Column 2 80.00%

b)

dividing row and column total with grand total
watch do not
drink 8% 42%
16% 84%
40% 53%
do not 12% 38%
24% 76%
60% 48%

c)

Applying chi square test of independence:
Expected Ei=row total*column total/grand total watch do not Total
drink 10.0000 40.0000 50.00
do not 10.0000 40.0000 50.00
total 20.00 80.00 100.00
chi square    χ2 =(Oi-Ei)2/Ei watch do not Total
drink 0.400 0.100 0.5000
do not 0.400 0.100 0.5000
total 0.8000 0.2000 1.000
test statistic X2 = 1.000

tDo not reject H0 Conclude that whether a person drinks wine and whether a person watches tennis are Independent
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