Computer & Data Analysis- Dr. Samir Safi & Mr. Ibrahim Abed
Midterm Exam 2- Nov. 26, 2013
Student’s Name:
Student ID #:
Question #1: (10 Points)
A chain of convenience stores wanted to test three different advertising policies:
 Policy 1: No advertising.
 Policy 2: Advertise in neighborhoods with circulars.
 Policy 3: Use circulars and advertise in newspapers.
Eighteen stores were randomly selected and divided randomly into three groups of six
stores. Each group used one of the three policies. Following the implementation of the
policies, sales figures were obtained for each of the stores during a 1-month period.
Using the SPSS output and   .05 , give an interpretation for each of the following:
1. (2 Points) Test of Homogeneity of Variances.
2. (2 Points) Explain in details the result of the ANOVA Table.
3. (6 Points) Discuss all the multiple comparisons.
1
SPSS Output for question #1
Test of Homogeneity of Variances
DATA
Levene
Statistic
.841
df1
df2
2
Sig.
.451
15
ANOVA
DATA
Between Groups
W ithin Groups
Total
Sum of
Squares
115.111
101.167
216.278
df
2
15
17
Mean Square
57.556
6.744
F
8.534
Sig.
.003
Multiple Comparisons
Dependent Variable: DATA
Bonferroni
(I) GROUP
Policy 1
Policy 2
Policy 3
(J) GROUP
Policy 2
Policy 3
Policy 1
Policy 3
Policy 1
Policy 2
Mean
Difference
(I-J)
-.6667
-5.6667*
.6667
-5.0000*
5.6667*
5.0000*
Std. Error
1.49938
1.49938
1.49938
1.49938
1.49938
1.49938
*. The mean difference is s ignificant at the .05 level.
2
Sig.
1.000
.005
1.000
.014
.005
.014
95% Confidence Interval
Lower Bound Upper Bound
-4.7056
3.3723
-9.7056
-1.6277
-3.3723
4.7056
-9.0389
-.9611
1.6277
9.7056
.9611
9.0389
Question #2: (10 Points)
An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in
the stomachs of sheep. A random sample of 24 worm- infected lambs of approximately the
same age and health was randomly divided into two groups. Twelve of the lambs were
injected with the drug and the remaining twelve were left untreated. After a 6-month
period, the lambs were slaughtered and the following worm counts were recorded:
Drug-Treated Sheep
18
43
28 50 16 32 13 35 38 33 6
7
Untreated Sheep
40
54
26 63 21 37 39 23 48 58 28 39
Using   .05 and the SPSS output, give an interpretation for each of the following:
a. (3 Points) What's the suitable statistical technique?
b. (7 Points) Test whether the mean number of tapeworms in the stomachs of the treated
lambs is less than the mean for untreated lambs. Assume the data is normally distributed for
each group.
3
SPSS Output for question #2
Group Statistics
Worm counts
CODING
Drug-Treated Sheep
Untreated Sheep
N
Mean
26.5833
39.6667
12
12
Std. Deviation
14.36193
13.85859
Std. Error
Mean
4.14593
4.00063
Independent Samples Test
Levene's Test for
Equality of Variances
F
Worm counts
Equal variances
as sumed
Equal variances
not ass umed
t-test for Equality of Means
Sig.
.205
t
.655
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-2.271
22
.033
-13.0833
5.76141
-25.03176
-1.13491
-2.271
21.972
.033
-13.0833
5.76141
-25.03264
-1.13403
Paired Samples Statistics
Pair
1
Drug-Treated Sheep
Untreated Sheep
Mean
26.5833
39.6667
N
12
12
Std. Error
Mean
4.14593
4.00063
Std. Deviation
14.36193
13.85859
Paired Samples Correlations
N
Pair
1
Drug-Treated Sheep
& Untreated Sheep
Correlation
12
.583
Sig.
.046
Paired Samples Test
Paired Differences
Mean
Pair
1
Drug-Treated Sheep
- Untreated Sheep
-13.0833
Std. Deviation
Std. Error
Mean
12.88733
3.72025
4
95% Confidence
Interval of the
Difference
Lower
Upper
-21.2716
-4.8951
t
-3.517
df
Sig. (2-tailed)
11
.005
Question #3: (5 Points)
Do rates of smoking decrease from pre-intervention to post-intervention? State your
hypotheses and explain in details your findings by using SPSS at 0.05 level?
SPSS Output for question #3
Paired Samples Statistics
Pair 1
Mean
30.53
5.43
Mean # of cigarettes smoked per day Pre-intervention
Mean # of cigarettes smoked following intervention
N
30
30
Std. Error
Mean
.987
1.108
Std. Deviation
5.406
6.067
Pa ired Sa mples Test
Mean
Pair 1 Mean # of cigarettes smoked per day Pre-intervention
25.100
- Mean # of cigarettes smoked following intervention
5
Paired Differences
95% Confidence Interval
of the Difference
Std. Error
Std. Deviation
Mean
Lower
Upper
7.402
1.351
22.336
27.864
t
18.574
df
Sig. (2-tailed)
29
.000
Question #4: (15 Points)
The data set BP contains blood pressure and other vital signs during various physical and
mental stressors.
Using   0.05 and the SPSS output, give an interpretation for each of the following:
a. (5 Points) Test the assumption of homogeneity
b. (15 Points) Does the mean of heart rate while immersing a hand in ice water (hrcp)
vary to a person's sex, parental hypertension (PH), or some combination of these
factors? Explain all related results.
6
SPSS Output for question #4
a
Le vene's Test of Equa lity of Error Va riances
Dependent Variable: heart rate cold pressor
F
1.352
df1
3
df2
176
Sig.
.259
Tests the null hypothes is that t he error variance of
the dependent variable is equal across groups.
a. Design: Int ercept+s ex+ ph+ sex * ph
Tests of Between-Subjects Effects
Dependent Variable: heart rate cold press or
Source
Corrected Model
Intercept
sex
ph
sex * ph
Error
Total
Corrected Total
Type III Sum
of Squares
1664.321a
1265221.332
1235.279
344.518
38.408
40744.540
1311649.000
42408.861
df
Mean Square
554.774
1265221.332
1235.279
344.518
38.408
231.503
3
1
1
1
1
176
180
179
F
2.396
5465.247
5.336
1.488
.166
Sig.
.070
.000
.022
.224
.684
a. R Squared = .039 (Adjus ted R Squared = .023)
Pa irw ise Com parisons
Dependent Variable: heart rate cold pressor
(I) subject sex
female
male
(J) subject sex
male
female
Mean
Difference
(I-J)
St d. Error
5.244*
2.270
-5. 244*
2.270
a
Sig.
.022
.022
95% Confidenc e Interval for
a
Difference
Lower Bound Upper Bound
.764
9.724
-9. 724
-.764
Based on estimated marginal means
*. The mean differenc e is significant at the .05 level.
a. Adjust ment for multiple comparisons: Bonferroni.
Pairwise Comparisons
Dependent Variable: heart rate cold press or
(I) parental hypertension
PH PH +
(J) parental hypertension
PH +
PH -
Mean
Difference
(I-J)
-2.769
2.769
Std. Error
2.270
2.270
a
Sig.
.224
.224
95% Confidence Interval for
a
Difference
Lower Bound Upper Bound
-7.250
1.711
-1.711
7.250
Based on estimated marginal means
a. Adjustment for multiple comparis ons : Bonferroni.
3. subject sex * parental hyperte nsion
Dependent Variable: heart rate cold pressor
subjec t sex
female
male
parent al hy pert ens ion
PH PH +
PH PH +
Mean
84.689
88.383
80.370
82.214
St d. Error
2.268
2.219
2.243
2.348
7
95% Confidenc e Interval
Lower Bound Upper Bound
80.213
89.165
84.003
92.763
75.942
84.797
77.581
86.848