7. Gender and Relationships. The Pew Internet and American Life Project examined
ID: 3205987 • Letter: 7
Question
7. Gender and Relationships. The Pew Internet and American Life Project examined whether single men and women differed with respect to their current relationships. The observed frequencies are given here. Test whether the type of relationship is independent of gender, using level of significance a 0.05. Gender Single men Single women Type of relationship 135 In committed relationship Not in committed relationship and not looking for partner 162 191 Not in committed relationship but looking for partner 19 Don't know/refused 18
Explanation / Answer
Null and Alternative Hypothesis:
H0: The type of relationship is independent of gender
H1: The type of relationship is dependent of gender
Level of significance is 5%
Test Statistics:
X^2 = S [ Oi – Ei ]^2 / Ei
Oi = Observed frequency
Ei = Expected frequency
(Oi – Ei):
Oi:
C1
C2
R1
135
138
R2
162
191
R3
89
84
R4
19
18
Ei:
C1
C2
R1
132.2548
140.7452
R2
171.0108
181.9892
R3
83.8098
89.1902
R4
17.9246
19.0754
(Oi – Ei):
C1
C2
R1
2.7452
-2.7452
R2
-9.0108
9.0108
R3
5.1902
-5.1902
R4
1.0754
-1.0754
(Oi – Ei)^2
C1
C2
R1
7.5362
7.5362
R2
81.1939
81.1939
R3
26.9381
26.9381
R4
1.1564
1.1564
(Oi –Ei)^2/Ei
C1
C2
R1
0.06
0.05
R2
0.47
0.45
R3
0.32
0.30
R4
0.06
0.06
Now we add all the values and we get it as 1.78
(4-1) * (2-1) = 3 degrees of freedom at 5% level of significance we get the critical value as 7.814. This value is more than the test value. We fail to reject the null hypothesis and there is sufficient evidence to conclude that type of relationship is independent of gender.
C1
C2
R1
135
138
R2
162
191
R3
89
84
R4
19
18
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.