Chi-Square Test for Independence A market researcher conducted a study to see if
ID: 2921168 • Letter: C
Question
Chi-Square Test for Independence
A market researcher conducted a study to see if different age groups prefer different news sources. He surveyed 100 people in the 18-49 age group and 80 people in the 50+ age group and asked them if they prefer to get their news from TV, online, radio, or printed newspapers. The data are listed in the table below. Conduct a Chi-Square test for Independence with = .01.
News source
Group 18-49
Group 50+
Total count
TV
40
50
90
Online
44
10
54
Radio
15
12
27
Printed papers
1
8
9
Total count
100
80
180
a) Calculate X2 statistic
b) Calculate the degree of freedom and then identify the critical value
c) Compare the X2 statistic with the critical value, then report the hypothesis test result, using “reject” or “fail to reject” the null hypothesis in the answer
d) Explain the conclusion in a sentence or two
News source
Group 18-49
Group 50+
Total count
TV
40
50
90
Online
44
10
54
Radio
15
12
27
Printed papers
1
8
9
Total count
100
80
180
Explanation / Answer
here null hypothesis: age and preference of medium of news are independent.
alternate hypothesis:age and preference of medium of news are dependent.
applying chi square test of independence on above data:
a) X2 statistic =26.400
b) degree of freedom =(number of rows-1)*(number of columns-1)=(4-1)*(2-1)=3
c) for 3 degree of freedom and 0.01 level critical value from X2 table =11.3449
as test stat is higher then critical value we reject null hypothesis
d) we have sufficient evidence at 0.01 level of significance that age and preference of medium of news are dependent.
Observed O Group 18-49 Group 50+ Total TV 40 50 90 Online 44 10 54 Radio 15 12 27 Printed papers 1 8 9 Total 100 80 180 Expected E=rowtotal*column total/grand total Group 18-49 Group 50+ Total TV 50.00 40.00 90 Online 30.00 24.00 54 Radio 15.00 12.00 27 Printed papers 5.00 4.00 9 Total 100 80 180 chi square =(O-E)^2/E Group 18-49 Group 50+ Total TV 2.0000 2.5000 4.500 Online 6.5333 8.1667 14.700 Radio 0.0000 0.0000 0.000 Printed papers 3.2000 4.0000 7.200 Total 11.733 14.667 26.400Related Questions
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