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:

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

2.) For each cell, calculate the corresponding cell, row, and column percentages

3.)Test the hypothesis that whether people drink wine is independent of whether people watch tennis. Set = .05.

Watch
Tennis Do Not
Watch Tennis Totals Drink Wine 12 38 50 Do Not Drink Wine 8 42 50 Totals 20 80 100

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =3.8415
since our test is right tailed,reject Ho when ^2 o > 3.8415
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 1
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415
we got | ^2| =1 & | ^2 | =3.8415
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.3173
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 1
critical value: 3.8415
p-value:0.3173
decision: do not reject Ho                              

col1 col2 row 1 12 38 50 row 2 8 42 50 TOTALS 20 80 N = 100

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