A researcher was interested in whether an individual's interest in politics was influenced by their level of education and sex. They recruited a random sample of participants to their study and asked them about their interest in politics, which they scored from 0 to 100, with higher scores indicating a greater interest in politics. The researcher then divided the participants by sex (Male/Female) and then again by level of education (High School/College/Advanced Degree).
(a) Conduct a complete analysis of variance on the data at the α=0.05 significance level. (20 points)
MGMT650-Doyle
Source df
SS
5525.2 975.2 6500.4
29.4 5328.1 167.7 975.2 6500.4
MS
1105.04 18.059
MS
29.4 2664.05 83.85 18.059
F
61.19
F
1.28 43 4.643
p-value
< 0.0001
p-value
0.207 < 0.0001 0.014
Treatments Error
Total
Source
Sex
Education Sex*Education Error
Total
5 54 59
df
1 2 2 54 59
SS
4
(b) Use the Tukey 95% simultaneous confidence intervals to determine which means are significantly different. (5 points)
MGMT650-Doyle
Difference
High School – College High School – Advanced
College – Advanced
Interval
(-8.6887, -2.2113) (-25.3887, -18.9113 (-13.6276, 9.97162)