Unit 1
Collecting Data and Drawing
Conclusions
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
1
Topic 1
Data and Variables
In-Class Activities
Activity 1-1: Student Data
1-1, 1-5, 2-7, 2-8, 3-7, 7-8
a.
Answers will vary.
b.
Answers will vary.
c.
No. Every word did not contain the same number of letters.
d.
The variable is the number of letters in each word.
e.
How many hours your slept in the past 24 = quantitative
Whether or not you slept for at least 7 hours = binary categorical
How many states you have visited = quantitative
Handedness = binary categorical, unless you classify ‘ambidextrous”, in which case, it is
not binary.
Day of the week on which you were born = categorical
Gender = binary categorical
Average study time per week = quantitative
Score on the first exam in this course = quantitative
f.
No. Neither average height of students in the class nor percentage of students in the class
who have used a cell phone can legitimately be considered variables when the observational
units are the students in your class. Both of these are numbers that provide summary information
about the class as a whole. They do not vary from student to student.
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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g.
If you record the average student height or percentage of student cell phone usage by
class taught at your school, these would become legitimate variables. Now these numbers would
(potentially) take on different values from class to class. The observational units are no longer
the students in your class, but rather all classes taught at your school.
Activity 1-2: Variables of State
a.
binary categorical variable
b.
not a variable
c.
quantitative variable
d.
quantitative variable
e.
binary categorical variable
f.
quantitative variable
g.
not a variable
Activity 1-3: Cell Phone Fraud
a.
The observational units are the cell phone calls.
b.
The binary categorical variables are direction, location, and whether the call took place
on a weekday or weekend. The non-binary categorical variable is day of week.
c.
The quantitative variables are duration of the call and time of day.
Activity 1-4: Studies from Blink
1-4, 5-14
a.
observational units = 100 CEOs; variable = height; type = quantitative
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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b.
observational units = 150 marriage counselors; variable = whether or not the counselor
makes the correct prediction about whether a couple will still be married in 5 years; type =
binary categorical.
c.
observational units = 200 African-American college students; variable 1= whether or not
their version of the exam asks them to indicate race; type = binary categorical; variable 2 = score
on SAT-like exam; type = quantitative
d.
observational units = 10 car dealerships; variable 1= gender of ‘customer’; type = binary
categorical; variable 2 = race of customer; type = binary categorical; variable 3 = price
negotiated for the car; type = quantitative
Activity 1-5: Student Data
1-1, 1-5, 2-7, 2-8, 3-7, 7-8
a.
Many answers are possible, but some examples include: Do male and female students
differ with regard to the number of states they have visited? Are sleeping times associated with
the day of the week on which a student was born?
b.
Answers will vary.
Activity 1-6: A Nurse Accused
1-6, 3-20, 6-10, 25-23
a.
The observational units are the eight-hour shifts.
b.
One variable is whether Gilbert worked on the shift. This variable is categorical and
binary. The other variable is whether a patient died on the shift. This variable is also categorical
and binary.
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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Homework Activities
Activity 1-7: Miscellany
a.
variable: binary categorical observational units: Pennies being spun
b.
variable: binary categorical observational unit: People leaving the washroom
c.
variable: quantitative observational units: Fast food sandwich
d.
variable: quantitative observational units: Residents of that Country
e.
variable: binary categorical observational units: American households
f.
variable: quantitative (though age might make more sense to interpret) observational
units: colleges
g.
variable: quantitative observational units: colleges
h.
variable: categorical observational units: American voters in 2004
i.
variable: binary categorical observational unit: newborn babies
j.
variable: quantitative observational units: Alfred Hitchcock movies
k.
variable: quantitative observational units: American pennies
l.
variable: quantitative observational units: automobiles
m.
variable: binary categorical observational units: automobiles
n.
variable: categorical observational units: automobiles
o.
variable: binary categorical observational units: applicants for graduate school
p.
variable: quantitative observational units: college students
q.
variable: categorical observational unit: person
r.
variable: binary categorical observational units: college students
s.
variable: binary categorical observational units: participants in sport
t.
variable: quantitative observational units: sport participants
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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u.
variable: quantitative observational units: states
v.
variable: quantitative observational units: bartenders
w.
variable: quantitative observational unit: person
x.
variable: quantitative observational units: brides
y.
variable: categorical observational units: brides
z.
variable: quantitative observational units: couples getting married.
Activity 1-8: Top 100 Films
a.
quantitative
b.
quantitative (though age might be easier to interpret)
c.
categorical
d.
binary categorical
e.
binary categorical
f.
binary categorical
g.
quantitative (notice how this quantity will vary from movie to movie)
Activity 1-9: Credit Card Usage
1-9, 16-12, 17-11, 19-8, 20-10
a.
year in school = categorical
whether or not the student has a credit card = binary categorical
outstanding balance on the credit card = quantitative
whether or not the outstanding balance exceeds $1000 = binary categorical
source for selecting a credit card = categorical
region of the country = categorical
b.
Answers will vary, but some sample questions include:
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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1) Which class (freshman, sophomore, …) tends to have the largest outstanding balance?
2) Do all regions of the country tend to obtain their credit cards from the same source?
Activity 1-10: Got a Tip?
1-10, 5-28, 14-12, 15-17, 22-4, 22-9, 25-3
a.
Answers will vary, but here are some examples:
The number of customers at each table
The amount spent on food and drink
Whether or not there were children at the table
Whether a man or woman paid the bill
b.
Which tends to have more influence on the tip – the size of the bill or the number of
people in the party?
Do males tend to be better tippers than females?
Activity 1-11: Proximity to the Teacher
1-11, 5-23, 27-9, 29-6
a.
observation unit = students
b.
1) variable = distance student is sitting from teacher (binary categorical)
2) variable = quiz scores (quantitative)
Activity 1-12: Emergency Rooms
a.
categorical
b.
quantitative
c.
categorical
d.
doesn’t vary from patient to patient so not a legitimate variable
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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e.
not a legitimate variable – you cannot ask an individual patient to tell you this
information.
f.
binary categorical
g.
quantitative
h.
binary categorical
i.
not a legitimate variable – needs to be worded as in “h” in order to be legitimate
j.
This is summary information about the emergency room – so not a legitimate variable.
Activity 1-13: Candy Colors
1-13, 2-19, 13-1, 13-2, 15-7, 15-8, 16-4, 16-22, 24-15, 24-16
a.
The observational units are the pieces of candy.
b.
The variable is the color of the candy. It is categorical (non-binary).
c.
Now the observational units are the samples of 25 pieces of candy.
d.
The variable is the proportion of the sample that is colored orange. It is quantitative.
Activity 1-14: Natural Light and Achievement
1-14, 5-17
a.
The observational units are the students.
b.
1) whether or not the student learned in natural light
2) score on standardized test
c.
1) binary categorical
2) quantitative
Activity 1-15: Children’s Television Viewing
1-15, 19-16, 20-4, 22-14, 22-15
a.
The observational units are the third and fourth grade students in San Jose.
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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b.
quantitative variables:

body mass index

triceps skinfold thickness

waist circumference

waist-to-hip ratio

weekly time spent watching television

weekly time spent playing video games
categorical variable: which school the student attends
Activity 1-16: Nicotine Lozenge
1-16, 2-18, 5-6, 9-21, 19-11, 20-15, 20-19, 21-6, 22-8
a.
The observational units are smokers.
b.
categorical variables:

whether they received the nicotine lozenge or placebo

gender

whether or not the person made a previous attempt to quit smoking

whether or not the subject successfully refrained from smoking during the study
c.
d.
quantitative variables

weight

number of cigarettes smoked per day
Type of lozenge assigned is a binary categorical variable.
Activity 1-17: Oscar Winners and Super Bowls
a.
Answers will vary from student to student. Some examples include:
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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categorical variables:
What is the movie’s genre? Did the picture also win an academy award for best director?
Quantitative variables:
What was the total length (in minutes) of the movie? What was the production cost of
the movie? How much did the movie gross during its first weekend of release?
b.
Answers will vary from student to student, but some examples include:
categorical variables:
In what city was the game played? Was the game played indoors or outdoors? Which
league was the winning team a member of? Was either team a wild card? Did the winner of the
coin toss win the game?
Quantitative variables:
What was the season percentage of wins for the winning team? What was the total
payroll for the winning team? How many people attended the game? What was the point
spread?
Rossman/Chance, Workshop Statistics, 3/e
Solutions, Unit 1, Topic 1
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