In a survey, 400 people are asked about their intention to purchase a certain pr
ID: 3314015 • Letter: I
Question
In a survey, 400 people are asked about their intention to purchase a certain product. At the 5% level. is there a dependence between gender and purchase intent? (WNB-“Willl not buy," MB-"Might buy," and WDB -"Will definitely buy.") If Ho is rejected, comment on the most important cell. MB Obs Men Womern WNB 35 100 MB 85 110 WDB 20 50 Exp Men Womern WNB WDB Ho: Cell WNB MB WDB Men Womern Hi: Test stat: Draw and label the curve denoting the decision rule: Decision (Reject or Fail to reject Ho) and interpretation: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: gender and purchase intent are independent
alternative, H1: gender and purchase intent are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =5.991
since our test is right tailed,reject Ho when ^2 o > 5.991
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 12.483
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991
we got | ^2| =12.483 & | ^2 | =5.991
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.002
ANSWERS
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null, Ho: gender and purchase intent are independent
alternative, H1: gender and purchase intent are dependent
test statistic: 12.483
critical value: 5.991
p-value:0.002
decision: reject Ho, claim that gender and purchase intent are dependent
MATRIX col1 col2 col3 TOTALS row 1 35 85 20 140 row 2 100 110 50 260 TOTALS 135 195 70 N = 400Related Questions
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