Statistics Homework Assignment: Solutions for Chapters 1, 2, 3, and 4

This document presents solutions to a statistics homework assignment, encompassing topics from chapters 1 through 4. The solutions address various concepts, including identifying experimental versus observational studies, analyzing frequency distributions and their shapes, comparing distributions (such as age distributions in a small town versus the U.S. population), calculating relative frequencies, and interpreting data related to majors and gender of graduates. Furthermore, the assignment covers measures of central tendency, like calculating the missing observation given the mean, and explores concepts of variability, including standard deviation, variance, and range, and their application in different scenarios, such as comparing SAT scores, patient ages, and motor skill reaction times. The document provides detailed answers and explanations for each problem, aiding in understanding statistical concepts.

Chapter1234
Student’s Name
Institution Affiliation

1.8. Indicating whether the study is an experiment or observation
Solutions
a. Observational
b. Observational
c. Experiment; variables are Sexual codes of primitive tribes(independent) and behavior
toward neighboring tribes(confounding variables)
d. Observational
e. Experiment; Variables are Reading comprehension scores(confounding variable) and
Number of months of formal education(independent variable)
f. Experiment; Variables are Graduate Record Exam(GRE) score(Confounding variable)
and cramming(independent variable)
g. Experiment; Variables are Attractive Score by panel of peer(confounding variable) and
Score on paper- and-pencil(independent variable)
h. Experiment; male attitude toward spending by federal government(independent variable)
and female attitude toward federal government spending(confounding variable)
i. Observational
1.9. Experiments and observational studies
a. what make studies to be experiment
Presence of control group
b. Confounding variables controlled by breastfeeding
 Adult intelligence
 Cognitive(IQ) development

2.14. Number of different residences occupied by graduating seniors during their college career
a. Frequency distribution
Number of Residences Frequency
1 1
2 6
3 8
4 5
5 1
6 1
7 1
9 1
Total 24
b. Shape of the distribution
The distribution is not bell shape, instead it’s data skewed to the left
2.17. Difference between two distributions; one reflection of the ages of all residents of small
town and the other reflecting the age of all U.S. residents.
a. Converting frequencies to %
AGE SMALL
TOWNf
SMALL TOWN
PERCENTAGE
U.S.POPULATION
(2010) (%)
65-above 105 21% 13%
60-64 53 11% 5%
55-59 45 9% 6%
50-54 40 8% 7%
45-49 44 9% 7%
40-44 38 8% 7%
35-39 31 6% 7%
30-34 27 5% 6%
25-29 25 5% 7%
20-24 20 4% 7%
15-19 20 4% 7%
10-14 19 4% 7%
5-9 17 3% 7%
0-4 16 3% 7%
500 100% 100%

b. Comparison
The small town has a higher number of aged residents (people aged 60 and above) than
US population. The percentage of people aged 60 and above (32%) is higher than that of
U.S. population (18%). However, U.S. has a youthful population than the small town.
The percentage of the persons aged 10 and below are more (21%) than those of small
town (10%)
c. frequency polygon
65-
abo
ve
60-
64
55-
59
50-
54
45-
49
40-
44
35-
39
30-
34
25-
29
20-
24
15-
19
10-
14
5-9 0-4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0%
5%
10%
15%
20%
25%
Frequency Polygon
AGE
U.S.POPULATIO
N(2010)( %)
SMALL TOWN
PERCENTAGE
Age
Relative Frequency
2.18. Bachelor degree earned in 2011-2012
a. Number of female psychology majors graduate in 2011-2012
83.6*1000=83, 600 persons

b. Relative frequencies
Major Field of
Study
Males Females Male Relative
Frequency (%)
Female Relative
Frequency (%)
Business 190 176.7 32% 22%
Social Sciences 90.6 87.9 15% 11%
Education 21.8 84 4% 10%
Health Sciences 24.9 138.6 4% 17%
Psychology 25.4 83.6 4% 10%
Engineering 81.3 17.3 14% 2%
Life Sciences 39.5 56.3 7% 7%
Fine Arts 37.2 58.6 6% 7%
Communication
s
33.5 55.2 6% 7%
Computer
Sciences
38.8 8.6 6% 1%
English 17 36.8 3% 5%
600 803.6 100% 100%
Males (32% and 6%) has a higher number of persons graduating with business and computer
science major than females (22% and 1%). There is more female graduation with health science
(17%) than males (4%).
c. Meaningfulness of calculating cumulative frequencies
It will not be meaningful as the number of males and females is in decimal form
d. Graph of Number of males and Females Graduates 2011-2012

Business
Social Sciences
Education
Health Sciences
Psychology
Engineering
Life Sciences
Fine Arts
Communications
Computer Sciences
English
0
40
80
120
160
200
Graph for the Number of Males and Females
Graduates 2011-2012
Males
Females
Major Field of Study
Number of Graduates
3.13
a. right skewed distribution
b. left skewed distribution
c. Normal and Symmetrical distribution
d. Positive skewed distribution.
3.14.
Scores Distance
from
mean
3 0
6 3
2 -1
0 -3
4 1
Mean 3 Sum of distance
from the mean
0

The mean dose not only identify points that satisfy the property shown in the table above
3.18. Given that mean is 5, what is the value of the missing observation
a. 1, 2, 10
missingvalue=5 ( 4 ) − ( 1+ 2+ 10 )=20−13=7
b. 2,4,1,5,7,7
missingvalue=5 ( 7 )− ( 2+2+1+5+7+7 )=35−24=11
c. 6,9,2,7,1,2
missingvalue=5 ( 7 )− ( 6+ 9+2+7+1+2 )=35−27=8
3.19 Association Population mean, sample mean or both
a. N : Populationmean
b. Varies: both Population and Sample mean
c. ∑: both Population and Sample mean
d. n: sample mean
e. Constant: population mean
f. Subset: Sample mean
4.9 Difference/ similarity in standard deviation
a. SAT scores for all graduating high school seniors (a1 or all college freshmen ( a2 )
Standard deviation will be different. The college freshmen will have a large standard deviation.
b. Ages of patients in a community hospital (b1) or a children hospital( b2
Standard deviation will be different. Ages of patient will have a large standard deviation
c. Motor skill reactions times of professional baseball players ( c1) or college student (c2
Standard deviation will be different. Motor skill reaction time of professional baseball player
will have a large standard deviation
d. GPAs of students at some university as revealed by a random sample( d1) or a census of
the entire student body(d2)

The Standard deviation can be approximated to be similar
e. Anxiety of a random sample of college students taken from the senior class(e1 or those
who plan to attend an anxiety-reduction clinic( e1).
Standard deviation will be different. or those who plan to attend an anxiety-reduction clinic(
e1).
Will have large standard deviation
f. Annual incomes of recent college graduates(f 1 or of 20-year alumni(f 2
Standard deviation will be different. Annual incomes of recent college graduates (f 1, will
have large standard deviation.
4.14.
Varianc
e
549.137
9
STDevd 23.4336
9
Range 112
IQR 23
The statistics of male weights indicated above are measures of variability. The four
measures are relatively and this suggests intermediate variability.
4.17. Why is standard deviation never negative?
Standard deviation is computed from sum of squared deviation (from the mean)
4.19. Solution
Male graduate will have maximum variability