3. In an experiment designed to measure the effect of sex and fre- quency of tra
ID: 3304412 • Letter: 3
Question
3. In an experiment designed to measure the effect of sex and fre- quency of travel on preference for foreign travel a 2 (sex) × 3 (frequency of travel) between-subjects design was adopted. Five respondents were assigned to each cell for a total sample size of 30. Preference for foreign travel was measured on a 9-point scale (1 = no preference, 9 = strong preference). Sex was coded as male = 1 and female 2, Frequency of travel was coded as light-1, medium 2, and heavy = 3, The data obtained are shown here Number Sex Travel Group Preference 2 4 4 4Explanation / Answer
Answer:
MINITAB used.
a).
Two-Sample T-Test and CI: preference, sex
Method
: mean of preference when sex = 1
µ: mean of preference when sex = 2
Difference: - µ
Equal variances are assumed for this analysis.
Descriptive Statistics: preference
sex
N
Mean
StDev
SE Mean
1
15
4.93
2.31
0.60
2
15
5.67
1.35
0.35
Estimation for Difference
Difference
Pooled
StDev
95% CI for
Difference
-0.733
1.892
(-2.149, 0.682)
Test
Null hypothesis
H: - µ = 0
Alternative hypothesis
H: - µ 0
T-Value
DF
P-Value
-1.06
28
0.298
Calculated t=-1.06, P=0.298 which is > 0.05 level. Ho is not rejected.
We conclude that there is no significant mean difference in preference between male and female.
b).
One-way ANOVA: preference versus Tralel Group
Method
Null hypothesis
All means are equal
Alternative hypothesis
Not all means are equal
Significance level
= 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor
Levels
Values
Travel Group
3
1, 2, 3
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Tralel Group
2
55.40
27.700
15.29
0.000
Error
27
48.90
1.811
Total
29
104.30
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
1.34578
53.12%
49.64%
42.12%
Means
Travel
Group
N
Mean
StDev
95% CI
1
10
4.600
1.897
(3.727, 5.473)
2
10
4.100
0.876
(3.227, 4.973)
3
10
7.200
1.033
(6.327, 8.073)
Pooled StDev = 1.34578
Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Tralel
Group
N
Mean
Grouping
3
10
7.200
A
1
10
4.600
B
2
10
4.100
B
Means that do not share a letter are significantly different.
Calculated F=15.29, P=0.000 which is < 0.05 level. Ho is rejected.
We conclude that there is significant mean difference in preference between 3 travel groups.
c).
General Linear Model: preference versus sex, Travel Group
Method
Factor coding
(-1, 0, +1)
Factor Information
Factor
Type
Levels
Values
sex
Fixed
2
1, 2
Travel Group
Fixed
3
1, 2, 3
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
sex
1
4.033
4.0333
4.94
0.036
Travel Group
2
55.400
27.7000
33.92
0.000
sex*Travel Group
2
25.267
12.6333
15.47
0.000
Error
24
19.600
0.8167
Total
29
104.300
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
0.903696
81.21%
77.29%
70.64%
From the Two way ANOVA, we infer that sex is significant, Travel group is significant and interaction between sex and travel group is significant.
: mean of preference when sex = 1
µ: mean of preference when sex = 2
Difference: - µ
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