1. Chi-square problem solutions
#10.4 and 10.6 (2/3e) or 9.4, 9.6 (1e)
Chi-square problem solutions

2. #10.4 2/3e (9.4 1e) Is there a gender gap in support for the Liberal Party?
Party Preference
Male
Female
Totals
Liberal 10
40% 15
60% 25
Other
100%
N = 50

3. #10.4 2/3e (9.4 1e) cont. Step 1: Step 2: H0: fo = fe H1: fo ≠ fe
Independent random samples
Level of measurement is nominal
Step 2:
H0: fo = fe H1: fo ≠ fe
Step 3:
Sampling Distribution = χ2
Alpha = .05
df = (r-1)(c-1) = 1
χ2 (critical) = 3.841

4. #10.4 2/3e (9.4 1e) cont.
Step 4: Find expected frequencies for each cell: fe =
cell 1: fe=25x25/50=12.5 cell 2: fe=25x25/50=12.5
cell 3: fe=25x25/50=12.5 cell 4: fe=25x25/50=12.5
Computational table to find χ2 (obtained):
Step 5: χ2obt.< χ2cr. Fail to reject Ho.
The % pattern shows that generally women prefer Liberals (60% vs 40%), but the association is not significant. fo fe
fo - fe
(fo - fe)2
(fo - fe)2 /fe 10
12.5
-2.5
6.25 .5 15
2.5
Total 50 -
Χ2 = 2.0

5. #10.6 2/3e (9.6 1e) Are pet therapy program participants more alert?
Alertness
Participants
Non-participants
Totals
High 23
67.6% 15
45.5% 38
Low 11
32.4% 18
54.5% 29 34
100% 33
N = 67

6. #10.6 2/3e (9.6 1e) cont. Step 1: Step 2: H0: fo = fe H1: fo ≠ fe
Independent random samples
Level of measurement is nominal
Step 2:
H0: fo = fe H1: fo ≠ fe
Step 3:
Sampling Distribution = χ2
Alpha = .05
df = (r-1)(c-1) = 1
χ2 (critical) = 3.841

7. #10.6 2/3e (9.6 1e) cont.
Step 4: Find expected frequencies for each cell: fe =
cell 1: fe=34x38/67=19.28 cell 2: fe=33x38/67=18.72
cell 3: fe=34x29/67= cell 4: fe=33x29/67=14.28
Computational table to find χ2 (obtained):
Step 5: χ2obt.< χ2cr. Fail to reject Ho.
The % pattern shows that generally participants are more alert (67.6% vs 45.5%), but the association is not significant. fo fe
fo - fe
(fo - fe)2
(fo - fe)2 /fe 23
19.28
3.72
13.838
.718 15
18.72
-3.72
.739 11
14.72
.940 18
14.28
.969
Total 67 -
Χ2 = 3.366

8. Going Further by Answering the 3 Questions Posed in Ch
Going Further by Answering the 3 Questions Posed in Ch. 11 in 2/3e (12 in 1e)
#9.4 (10.4) Liberal Party support by gender
Is there an association? Not a significant association.
How strong is the association?
Calculate Phi = A moderate association (table 11.12/12.12)
What is the pattern of the association?
Generally the pattern of percentages shows that females are more likely to support the Liberal Party (60% vs 40%).

9. Going Further cont. #9.6 (10.6) Alertness by program participation
Is there an association? Not a significant association.
How strong is the association?
Calculate Phi = A moderate association (table 11.12/12.12)
What is the pattern of the association?
Generally the pattern of percentages shows that program participants are more alert (67.6% vs 45.5%).