Use the data below to answer the questions. id Education Approve of cohabitation
ID: 3316409 • Letter: U
Question
Use the data below to answer the questions.
id
Education
Approve of cohabitation
id
Education
Approve of cohabitation
1
HS or more
Yes
16
HS or more
No
2
HS or more
No
17
HS or more
Yes
3
HS or more
Yes
18
Less than HS
Yes
4
HS or more
Yes
19
Less than HS
Yes
5
Less than HS
No
20
HS or more
Yes
6
HS or more
Yes
21
Less than HS
No
7
HS or more
Yes
22
HS or more
Yes
8
HS or more
Yes
23
Less than HS
Yes
9
Less than HS
No
24
HS or more
Yes
10
HS or more
Yes
25
HS or more
Yes
11
HS or more
No
26
Less than HS
No
12
HS or more
Yes
27
Less than HS
No
13
HS or more
Yes
28
HS or more
Yes
14
HS or more
No
29
HS or more
No
15
Less than HS
Yes
30
Less than HS
Yes
a) Construct a bivariate table with frequencies and column percentages. Based on the percentages, is there an association between education and attitudes toward cohabitation? Describe the pattern of association.
b) Assuming that this is a random sample, test a hypothesis (use = 0.05) that there is an association between one’s education and attitudes toward cohabitation. Show all your work (state the hypotheses, find the critical value, compute the test statistics, state a conclusion) and write one-two sentences summarizing the results. (Hint: do a chi-square test)
c) Is this association weak, moderate or strong? Compute and interpret Phi statistics.
id
Education
Approve of cohabitation
id
Education
Approve of cohabitation
1
HS or more
Yes
16
HS or more
No
2
HS or more
No
17
HS or more
Yes
3
HS or more
Yes
18
Less than HS
Yes
4
HS or more
Yes
19
Less than HS
Yes
5
Less than HS
No
20
HS or more
Yes
6
HS or more
Yes
21
Less than HS
No
7
HS or more
Yes
22
HS or more
Yes
8
HS or more
Yes
23
Less than HS
Yes
9
Less than HS
No
24
HS or more
Yes
10
HS or more
Yes
25
HS or more
Yes
11
HS or more
No
26
Less than HS
No
12
HS or more
Yes
27
Less than HS
No
13
HS or more
Yes
28
HS or more
Yes
14
HS or more
No
29
HS or more
No
15
Less than HS
Yes
30
Less than HS
Yes
Explanation / Answer
Result:
a) Construct a bivariate table with frequencies and column percentages. Based on the percentages, is there an association between education and attitudes toward cohabitation? Describe the pattern of association.
Approve of cohabitation
No
Yes
Grand Total
Education
HS or more
5
15
20
Less than HS
5
5
10
Grand Total
10
20
30
Column percentages
No
Yes
Grand Total
HS or more
50
75
66.67
Less than HS
50
25
33.33
Grand Total
100
100
100
It seems that there an association between education and attitudes toward cohabitation. Higher the education associated with approval of cohabitation.
b) Assuming that this is a random sample, test a hypothesis (use = 0.05) that there is an association between one’s education and attitudes toward cohabitation. Show all your work (state the hypotheses, find the critical value, compute the test statistics, state a conclusion) and write one-two sentences summarizing the results. (Hint: do a chi-square test)
Ho: There is no association between one’s education and attitudes toward cohabitation
H1: There is an association between one’s education and attitudes toward cohabitation
Chi-Square Test
Observed Frequencies
Column variable
Calculations
No
Yes
Total
fo-fe
HS or more
5
15
20
-1.6667
1.6667
Less than HS
5
5
10
1.6667
-1.6667
Total
10
20
30
Expected Frequencies
Column variable
0
No
Yes
Total
(fo-fe)^2/fe
HS or more
6.6667
13.3333
20
0.4167
0.2083
Less than HS
3.3333
6.6667
10
0.8333
0.4167
Total
10
20
30
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841
Chi-Square Test Statistic
1.8750
p-Value
0.1709
Do not reject the null hypothesis
Calculated chi square = 1.875 is < critical chi square value 3.841 at 0.05 level of significance.
Ho is not rejected.
We conclude that there is no association between one’s education and attitudes toward cohabitation
c) Is this association weak, moderate or strong? Compute and interpret Phi statistics.
Phi statistics = sqrt(1.875/30)=0.25
This association is weak.
Approve of cohabitation
No
Yes
Grand Total
Education
HS or more
5
15
20
Less than HS
5
5
10
Grand Total
10
20
30
Column percentages
No
Yes
Grand Total
HS or more
50
75
66.67
Less than HS
50
25
33.33
Grand Total
100
100
100
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