PROBLEM1: The data below shows the Number of absences X and the Final Grade, Y of seven students in the statistics class.
|
Student
|
Number of absences x
|
Final Grade y
|
|
A
|
6
|
82
|
|
B
|
2
|
86
|
|
C
|
15
|
43
|
|
D
|
9
|
74
|
|
E
|
12
|
58
|
|
F
|
5
|
90
|
|
G
|
8
|
78
|
a.
The relationship is linear. The negative slope shows that the relationship is negative; the more number of absences the lower the grade.
b.
|
|
X
|
Y
|
XY
|
X2
|
Y2
|
|
6
|
82
|
492
|
36
|
6724
|
|
2
|
86
|
172
|
4
|
7396
|
|
15
|
43
|
645
|
225
|
1849
|
|
9
|
74
|
666
|
81
|
5476
|
|
12
|
58
|
696
|
144
|
3364
|
|
5
|
90
|
450
|
25
|
8100
|
|
8
|
78
|
624
|
64
|
6084
|
|
SUM
|
57
|
511
|
3745
|
579
|
38993
|
r = (7*3745-57*511)/squareroot[(7*579-572)*(7*38993-5112)] =
= -2912/squareroot(804*11830)=-2912/3084.043= -.944
The correlation coefficient is -.944: It shows a very strong, negative relationship between the number of absences and the obtained grades.
r2 = 89.15%. It represents the percent of the variances in the values of Y that can be explained by knowing the value of X. 89.15% of the variation of Y (number of absences) is explained by X (grades) and 10.85% is unexplained.
PROBLEM 2: The data below shows the reading (x) and math scores (y) of students.
|
Reading Scores
|
Math Scores
|
|
1
|
4
|
|
2
|
3
|
|
3
|
8
|
|
3
|
6
|
|
4
|
7
|
|
5
|
7
|
|
6
|
8
|
|
7
|
8
|
|
7
|
9
|
|
8
|
10
|
|
8
|
9
|
|
9
|
8
|
PROBLEM 3
The data below shows the score on a promotion test given to police officers and the number of hours studied. Calculate the correlation coefficient.
|
Hours Studied
|
Score on promotion test
|
|
0
|
0
|
|
1
|
1
|
|
2
|
1
|
|
3
|
2
|
|
4
|
5
|
|
6
|
6
|
|
12
|
8
|
|
16
|
10
|
PROBLEM 4: An emergency service wishes to see whether there a relationship exists between the outside temperature and the number of emergency calls it receives for a 7 hours period. The data is shown below.
Temperature x | 68 74 82 88 93 99 101
Number of calls | 7 5 7 9 11 12 15
PROBLEM 5:
A company that manufactures small lathes is interested in establishing standards for employees. A random sample of 18 employees is selected in order to develop the standards. The data collected is below.
A manager at the firm feels that assembly time is related to intelligence. She feels that employees who did well in high school (as measured by high school averages) should be able to do the job faster. Does the data support her hunch?
|
high school
average
|
Time to
assemble lathe
(minutes)
|
|
50
|
52
|
|
62
|
53
|
|
65
|
62
|
|
68
|
70
|
|
71
|
73
|
|
73
|
78
|
|
75
|
80
|
|
79
|
82
|
|
80
|
85
|
|
82
|
86
|
|
83
|
90
|
|
85
|
94
|
|
88
|
95
|
|
90
|
106
|
|
90
|
111
|
|
94
|
120
|
|
94
|
139
|
|
100
|
145
|