1. Practice Questions for ANOVA
#9.2 a, b, c (2/3e)
#8.2 a, b, c (1e)

2. #9.2 a (8.2 a) Involvement by Education
Does involvement vary by education?
Step 1:
Independent Random Samples, Interval-Ratio
Populations normally distributed, variances are equal
Step 2:
H0: μ1 = μ2= μ3
H1: At least one mean is different
Step 3:
Sampling Distribution = F distribution
Alpha = 0.05
dfw = (n – k) = 15-3 = 12
dfb = k – 1 = 2
F(critical) = 3.88

3. #9.2 a (8.2 a) Involvement by Education cont.
Computational Table:
Grand Mean = nt=15
< high school
n=5
High school
Coll./University
∑Xi 10 16 15
∑X2 30 60 57
Group Means 2
3.2 3

4. #9.2 a (8.2 a) Involvement by Education cont.
Step 4:
SSW = SST-SSB = =
MSB = SSB/dfb = 4.135/2 = 2.068
MSW = MSB/dfw = /12 = 2.574
Fobt = MSB/MSW = 2.068/2.574 = .803
Step 5: Fobt<Fcr. Fail to reject H0. Involvement does not vary by education.

5. #9.2 b (8.2 b) Involvement by Residence
Does involvement vary by length of residence?
Step 1:
Independent Random Samples, Interval-Ratio
Populations normally distributed, variances are equal
Step 2:
H0: μ1 = μ2= μ3
H1: At least one mean is different
Step 3:
Sampling Distribution = F distribution
Alpha = 0.05
dfw = (n – k) = 15-3 = 12
dfb = k – 1 = 2
F(critical) = 3.88

6. #9.2 b (8.2 b) Involvement by Residence cont.
Computational Table:
Grand Mean = nt=15
< 2 years
n=5
2 – 5 years
> 5 years
∑Xi 12 14 15
∑X2 42 54 51
Group Means
2.4
2.8 3

7. #9.2 b (8.2 b) Involvement by Residence cont.
Step 4:
SSW = SST-SSB = =
MSB = SSB/dfb = .935/2 = .467
MSW = MSB/dfw = /12 = 2.856
Fobt = MSB/MSW = .467/2.856 = .164
Step 5: Fobt<Fcr. Fail to reject H0. Involvement does not vary by length of residence.

8. #9.2 c (8.2 c) Involvement by TV Viewing
Does involvement vary by amount of TV watched?
Step 1:
Independent Random Samples, Interval-Ratio
Populations normally distributed, variances are equal
Step 2:
H0: μ1 = μ2= μ3
H1: At least one mean is different
Step 3:
Sampling Distribution = F distribution
Alpha = 0.05
dfw = (n – k) = 15-3 = 12
dfb = k – 1 = 2
F(critical) = 3.88

9. #9.2 c (8.2 c) Involvement by TV Viewing cont.
Computational Table:
Grand Mean = nt=15
Little or none
n=5
Moderate
High
∑Xi 4 16 21
∑X2 6 52 89
Group Means
0.8
3.2
4.2

10. #9.2 c (8.2 c) Involvement by TV Viewing cont.
Step 4:
SSW = SST-SSB = = 4.672
MSB = SSB/dfb = /2 =
MSW = MSB/dfw = 4.672/12 = .389
Fobt = MSB/MSW = /.389 =
Step 5: Fobt>Fcr. Reject H0. Involvement varies significantly by TV viewing (F=39.25, df=2,12, α=.05)

11. #9.2 d (8.2 d) Involvement by Number of Children
Try this one yourself!
(Your answer should be Fobt = 2.32)