A market researcher conducted a study to see if different age groups prefer diff
ID: 2922573 • Letter: A
Question
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
What are the variables in this analysis? What type of variable is each (nominal, ordinal, or continuous)? (2 points total: 1 for each variable- .5 for variable name, .5 for variable type)
State the null and alternative hypotheses in words (2 points total: 1 for each hypothesis)
Calculate X2 statistic (3 points total: 1 for final answer, 1 for setting up correct table, 1 for calculation- deduct .5 for each calculation error)
Calculate the degree of freedom and then identify the critical value (2 points total: 1 for df, 1 for critical value)
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 (1 point total: .5 for each answer)
Explain the conclusion in a sentence or two (1 point)
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
variable --frequency distribution preference of different news sources
type of variable ---nominal
null hypothesis: age group and type of news media are independent
alternate hypothesis:age group and type of news media are dependent
from above X2 statistic =26.4
degree of freedom =(number of rows-1)*(number of columns-1) =(4-1)*(2-1)=3
for 3 df and 0.01 level of signficance critical value =11.3449
as test statsitic is higher then critical value “reject” the null hypothesis
we have sufiicient evidence to conclude that age group and type of news media are dependent
Observed O 18-49 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 18-49 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 18-49 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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