1. In a study by Wang et al., researchers examined bone strength. They collected
ID: 3203911 • Letter: 1
Question
1. In a study by Wang et al., researchers examined bone strength. They collected 10 cadaveric femurs from subjects in three age groups: young (19-49 years), middle-aged (50-69 years), and elderly (70 years or older) [Note: one value was missing in the middle-aged group]. One of the outcome measures (W) was the force in Newtons required to fracture the bone. The results are presented below:
Young (Y)
Middle-aged (MA)
Elderly (E)
193.6
125.4
59.0
137.5
126.5
87.2
122.0
115.9
84.4
145.4
98.8
78.1
117.0
94.3
51.9
105.4
99.9
57.1
99.9
83.3
54.7
74.0
72.8
78.6
74.4
83.5
53.7
112.8
96.0
Test the hypothesis to see if you can conclude that there is a difference among population means. Let = .05. Use Tukey’s HSD procedure to test for significant differences among individual pairs of means. (20 marks) Note: Use SPSS Data1 to answer the question
1.Inn a study by Wang et al., researchers examined bone strength. They collected 10 cadaveric femurs from subjects in three age groups: young (19-49 years), middle-aged (50-69 years), and elderly (70 years or older) [Note: one value was missing in the middle-aged group]. One of the outcome measures (W) was the force in Newtons required to fracture the bone. The results are presented below
Wheelchair Use
Yes
No
Fallers
62
121
Nonfallers
18
32
Do these data provide sufficient evidence to warrant the conclusion that wheelchair use and falling are related? Let = .05 (15 marks)
Note: Use SPSS Data 2 to answer the question
2.Kindergarten students were the participants in a study conducted by Susan Bazyk et al. The researchers studied the fine motor skills of 37 children receiving occupational therapy. They used an index of fine motor skills that measured hand use, eye-hand coordination, and manual dexterity before and after 7 months of occupational therapy. Higher values indicate stronger fine motor skill. The scores appear in the following table.
Subject
Pre
Post
Subject
Pre
Post
1
91
94
20
76
112
2
61
94
21
79
91
3
85
103
22
97
100
4
88
112
23
109
112
5
94
91
24
70
70
6
112
112
25
58
76
7
109
112
26
97
97
8
79
97
27
112
112
9
109
100
28
97
112
10
115
106
29
112
106
11
46
46
30
85
112
12
45
41
31
112
112
13
106
112
32
103
106
14
112
112
33
100
100
15
91
94
34
88
88
16
115
112
35
109
112
17
59
94
36
85
112
18
85
109
37
88
97
19
112
112
Can one conclude on the basis of these data that after 7 months, the fine motor skills in a population similar subjects would be stronger? Let a = .05. Determine the p value. (15 marks)
Note: Use SPSS to answer the question
3.The following are the pulmonary blood flow (PBF) and pulmonary blood volume (PBV) values recorded for 16 infants and children with congenital heart disease:
y
PBV (ml/sqM)
167
280
394
420
303
429
602
522
224
291
233
370
531
516
211
439
X
PBF (L/min/sqM)
4.32
3.40
6.25
17.30
12.30
13.99
8.74
8.90
5.87
5.00
3.51
4.24
19.41
16.61
7.21
11.60
Find the regression equation describing the linear relationship between the two variables. Let = .05.
(15 marks)
Note: Use SPSS to answer the question
In a study of the relationship between creatinine excretion, height, and weight, the data shown in the following table were collected on 20 infant males:
Creatinine
Excretion
(mg/day)
Weight (kg)
Height (em)
Infant
y
X1
X2
1
105
9
72
2
115
11
76
3
53
6
59
4
85
8
67
5
135
10
60
6
58
5
58
7
90
8
70
8
60
7
65
9
45
4
54
10
125
11
83
11
86
7
64
12
80
7
66
13
65
6
61
14
95
8
66
15
25
5
57
16
125
11
81
17
40
6
59
18
95
9
71
19
70
6
62
20
120
10
75
(a) Find the multiple regression equation describing the relationship among these variables. (15 marks)
(b) Let X1 = 9 and X 2 = 58 and find the predicted value of Y. (5 marks)
Note: Use SPSS to answer the question
6.LaMont et al. tested for obstructive coronary artery disease (OCAD) among 113 men
and 35 women who complained of chest pain or possible equivalent to their primary care
physician. Following Table shows the cross-classification of OCAD with gender. We wish to
use logistic regression analysis to determine how much greater the odds are of finding
OCAD among men than among women. (15 marks)
Table: Cases of Obstructive Coronary Artery Disease (OCAD) classified by sex
Disease
Males
Females
Total
OCAD present
92
15
107
OCAD not present
21
20
41
Total
113
35
148
Note: Use SPSS to answer the question
Young (Y)
Middle-aged (MA)
Elderly (E)
193.6
125.4
59.0
137.5
126.5
87.2
122.0
115.9
84.4
145.4
98.8
78.1
117.0
94.3
51.9
105.4
99.9
57.1
99.9
83.3
54.7
74.0
72.8
78.6
74.4
83.5
53.7
112.8
96.0
Explanation / Answer
Result: first problem solved.
(a) Find the multiple regression equation describing the relationship among these variables. (15 marks)
SPSS OUTPUT
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.937a
.878
.863
11.584
a. Predictors: (Constant), x2, x1
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
16383.688
2
8191.844
61.050
.000b
Residual
2281.112
17
134.183
Total
18664.800
19
a. Dependent Variable: y
b. Predictors: (Constant), x2, x1
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
12.287
30.451
.403
.692
x1
16.250
2.652
1.117
6.126
.000
x2
-.812
.707
-.209
-1.147
.267
a. Dependent Variable: y
The regression equation is
Y=12.287+16.250*x1-0.812*x2
(b) Let X1 = 9 and X 2 = 58 and find the predicted value of Y. (5 marks)
Predicted y = 12.287+16.250*9-0.812*58
=111.441 (mg/day)
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.937a
.878
.863
11.584
a. Predictors: (Constant), x2, x1
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