Assignment 2
ECON 306
Total Point: 30
Due date: Saturday May 18, 2024
Time: 11:59PM
Submission: Online (via Canvas)
Format: PDF and Excel
Instruction.
- This is an individual assignment. Identical works will not be graded.
- Submit PDF file and Excel file that you use to calculate
Textbook:
Applied Statistics in Business and Economics, 5th Edition, Doane, David P., and Lori E.
Seward., Mcgraw-Hill, 2016.
Exercise 1.
A. Below are five questions from a survey of MBA students. Answers were written in the blank at the
left of each question. For each question, state the data type (categorical, discrete numerical, or
continuous numerical) and measurement level (nominal, ordinal, interval, ratio). Explain your
reasoning. If there is doubt, discuss the alternatives.
What is your gender? (Male = 0, Female = 1)
What is your approximate undergraduate college GPA? (1.0 to 4.0)
About how many hours per week do you expect to work at an outside job this semester?
What do you think is the ideal number of children for a married couple?
On a 1 to 5 scale, which best describes your parents? 1 = Mother clearly dominant ↔ 5 =
Father clearly dominant
_____ Q1
_____ Q2
_____ Q3
_____ Q4
_____ Q5
B. (a) Give three original examples of discrete data. (b) Give three original examples of continuous
data. In each case, explain and identify any ambiguities that might exist. Hint: Do not restrict
yourself to published data. Consider data describing your own life (e.g., your sports performance,
financial data, or academic data). You need not list all the data, merely describe them and show a
few typical data values.
Exercise 2.
Which measurement level (nominal, ordinal, interval, ratio) is each of the following variables? Explain.
a.
b.
c.
d.
e.
f.
Number of passengers on Delta Flight 833.
Waiting time (minutes) after gate push back before Delta Flight 833 takes off.
Brand of cell phone owned by a cabin attendant on Delta Flight 833.
Ticket class (first, business, or economy) of a randomly chosen passenger on Delta Flight 833.
Outside air temperature (Celsius) when Delta Flight 833 reaches 35,000 feet.
Passenger rating (on 5-point Likert scale) of Delta’s in-flight food choices.
36
Applied Statistics in Business and Economics
probability of being selected as the items we chose at the beginning of the sampling process.
This could lead to a bias (a tendency to overestimate or underestimate the parameter we are
trying to measure) in our sample results. Sampling with replacement does not lead to bias.
When should we worry about sampling without replacement? Only when the population
is finite and the sample size is close to the population size. Consider the Russell 3000® Index,
which has 3000 stocks. If you sample 100 stocks, without replacement, you have “used” only
Exercise 3.
about 3 percent of the population. The sample size n 5 100 is considered small relative to the
population size N 5 3000. A common criterion is that a finite population is effectively infinite
The target population is all stocks
in the S&P
Is each
the following
a parameter
statistic?
if the sample
is less500
thanindex.
5 percent
of theofpopulation
(i.e., if
nyN # .05).or
InaChapter
8, you
will learn how to adjust for the effect of population size when you make a sample estimate.
For now, you ratio
only need
to recognize
thatinsuch
a. The average price/earnings
for all
500 stocks
the adjustments
S&P index.are of little consequence when the
population
is
large.
b. TheproportionofallstocksintheS&P500indexthathadnegativeearningslastyear.
c. The proportion of energy-related stocks in a random sample of 50 stocks.
nite for
Population?
d. The average rateInfi
of return
20 stocks recommended by a broker.
Chapter 2
Final PDF
Data Collection
PDF
When the sample is less than 5 percent of the population (i.e., when nyN # Final
.05), then
the to printer
Exercise 4. See Section 2.4.
Sampling Methods of the Textbook.
2.20 Suppose you want
to studyis the
numberinfi
of nite.
e-mail
by students
your statistics
population
effectively
An accounts
equivalentowned
statement
is that a in
population
is effectively
whenisititisifatyou
least
times each
as large
as thewho
sample
whenID
Nyn
$ 20).endclass. What kindinfi
ofnite
sample
(a)20survey
student
has (i.e.,
a student
number
Below is a 6 x 8ing
array
of all
moviegoers.
a population.
random
in ancontaining
odd number.the
(b)ages
survey
the students Treat
sitting this
in theasfront
row, and (c)Select
survey aevery
fifth sample
of 10 moviegoers’
ages
by
using
(a)
simple
random
sampling
with
Excel’s
=
RANDBETWEEN(
) function
student who arrives at the classroom?
Because computers are easier, we rarely use random number tables. Table 2.6 shows a
(see Option
A in
2.6
below),
(b)
simple between
random
sampling
with
Excel’s
=
2.21 Below
is a 6 Table
3few
8 array
containing
thetoages
of moviegoers
file 1 and
Hunger
Games).
Treaton
this
alternative
ways
choose
10 integers(see
875. All
are based
a software
INT(1+max(Data)*RAND())
function
(see
Option
B
in
Table
2.6
below),
(c)
systematic
sampling,
(d)
as a population.algorithm
Select
a random
sample
of
10
moviegoers’
ages
by
using
(a)
simple
random
sampling
that creates uniform decimal numbers between 0 and 1. Excel’s function =RAND( )
sampling,
(e)does
convenience
sampling.
Explain
your
methods.
with a and
random
number
simple
random
sampling
with
Excel’sfunction.
=RANDBETWEEN(
(c)
this,table,
and (b)
many
pocket
calculators
have
a similar
We call) function,
these pseudorandom
s in Business andjudgment
Economics
systematic sampling,
(d) judgment
sampling,
and algorithms
(e) convenience
sampling.
Explain
your methods.
generators
because even
the best
eventually
repeat
themselves
(after a cycle of
millions
of numbers).
Thus,
random
data encryption
scheme
could conceiv32
34
33
12 a software-based
57
13
58
16
the number
of days
on the
market35for Intel
the 36
recent home
sales20in the
city of
ably
and
hardware-based
ISES 3.4 (a) The table shows
23
23 be broken.
62 To enhance
65 data security,
15 other firms
17 are examining
methods
(e.g.,
based
on
thermal
noise
or
radioactive
decay)
to
prevent
patterns
or
repetition.
Sonando Hills. Construct
a frequency
and31histogram,
nice (round)
14
11
51 distribution
33
13 using 11
58 bin limits.
Fortunately, most applications don’t require that degree of randomness. For example, the iPod
(b) Describe the 23
distribution
features.
10 and note
63 any unusual
34
12
15Homes62
13
Shuffle’s song choices are not strictly random because its random numbers are generated by
40
11
18
62
64
30
42
20 repeat period is so
an algorithm from a “seed number” that eventually repeats. However, the
18
70
86 notice.
12149 and MINITAB’s
86 random
21
5652 that an 11
51 never
38
15
21 3numbers66
great
iPod17
user would
Excel’s
are good
enough
for
most
purposes.
In the previous
what was the 26
proportion of all2848 moviegoers6 who were55under age21
96 2.22 (a)41
50 population,176
30? (b) For each of the samples of size n 5 10 that you took, what was the proportion of moviegoers
TABLE
43 2.6 under
20 age 30? (c)Excel—Option
56
16
20 into 1030spreadsheet
31 cells.
Was each sample
closefunction
to the population
proportion?
Enter the57
Excel
=RANDBETWEEN(1,875)
A71 proportion
3.5
Pressfor
F9 to
new friends
sample. into cells B1:B10. Choose three
Some Ways
In 44
Excel, type a92
list containing
10
of ayour
44 2.23to Get
179 names
80get
98
44
66
15
10 Random Integers
Enter
the
function
=INT(1+875*RAND())
10A1:A10,
spreadsheet
cells.
Excel—Option
B
names at random by randomizing this list. To do this, enter =RAND( ) intointo
cells
copy
thePress F9
between 1 and 875
to get a new sample.
random column and paste it using Paste Special > Values to fix the random numbers, and then sort
The
website
Internet
www.random.org
give
you many kinds
of excellent in
(a) The table shows
oncolumn.
a stateThe
civil
exam
bywill24sample.
applicants
for positions
the list raw
by thescores
random
firstservice
three names
aretaken
the random
random numbers (integers, decimals, etc).
law enforcement. Construct a frequency distribution and histogram, using nice (round) bin limits.
MINITAB
Use MINITAB’s Random Data menu with the Integer option.
(b) Describe
distribution
and note any unusual
features.
Civil
2.5theDATA
SOURCES
Pocket Calculator
83
Press the RAND key to get a random number in the interval [0,1],
multiply by 875, then round up to the next integer.
93
74
98
85
82
79
78
LO
One goal of a statistics course is to help you learn where to find data that might be needed.
82 Fortunately,
68 many excellent
67
82 are widely78available, either
83 in libraries
70 or through
99 private
sources
Find everyday prin
Randomizing
aofList
purchase.
Table
2.10
summarizes
a
few
them.
electronic
data sou
18
96Section 3.2.
93 of the textbook.
62
64
93
27
58
Exercise
5.The
See
U.S.
Census Bureau
and the U.S. Bureau of Labor Statistics are rich sources of data on
To randomize a list (assuming it is in a spreadsheet) we can insert the Excel function
many different aspects
of life in the United States. The publications library supported by the
=RAND( ) beside each row. This creates a column of random decimal numbers between
3.6 (a) MakeCensus
a frequency
and
histogram (using
appropriate
bins) for
these
28reports
observaBureau distribution
can 0beand
found
at www.census.gov.
annual
1. Copy
the random numbersThe
and monthly,
paste themquarterly,
in the sameand
column
using
Paste Special >
by spent
the Bureau
of
Labor
statistics
be found
at www.bls.gov.
Itsort
should
noted
tions on published
the amount
for dinner
four
in can
downtown
Chicago
on Then
Friday
night.
(b)
Repeat
Values
to “fi
x” for
them
(otherwise
they
will keep
changing).
all thebecolumns
by the
that until
2012,
the Statistical
Abstract
of the
United
theWhy?
largest,The
most
random
number
and
voilà—the
list was
is now
random!
fiDinner
rstgeneral,
n items and
on the ranthe exercise,
using
a different
number
ofcolumn,
bins.
Which
isStates
preferred?
domized
list can now
be used
random
sample.
This
methodAis2012
especially
useful
freely available annual
compendium
of facts
andasfiagures
from
public
sources.
review
of when
the by
list the
is very
long
(perhaps
of lines).
The fiarst
n items113
are
a random
sample
95 publications
103sponsored
109
170millions
114
107of the
U.S.
Census
Bureau
concluded
with
decision
to quit
publishing
entire list, for they
as likely
as any previous
others. years’ publications at the U.S.
youarecan
still access
124 the Statistical
105 Abstract. However,
80
104
84
176
115
Census website.
69
95 and monthly134
108
61 Economic Report
160 of the Presi128
For annual
time series economic
data, try the
68 dent (ERP),95which is published
61 every February.
150 The tables52in the ERP can87be downloaded
136
for free in Excel format. Data on cities, counties, and states can be found in the State and
Metropolitan Area Data Book, published every few years by the Bureau of the Census and
3.7 (a) Makeavailable
a frequency
distribution
histogram for the monthly off-campus rent paid by
on CD-ROM
in many and
libraries.
doa37304_ch02_022-055.indd 36
11/21/14 5:07 PM
30 students.Annual
(b) Repeat
the from
exercise,
using
a different
ofmost
bins.bookstores.
Which is These
preferred?
Why?
almanacs
several
major
publishersnumber
are sold at
include
data reprinted from the above sources, but also information on recent events, sports, stock marRents
ket, elections, Congress, world nations, states, and higher education. One of these almanacs
730 should be on every
730 informed citizen’s
730 shelf.
930
700
570
690
1,030
Type of Data
740
Examples
620
720
670
TABLE 2
learn how Excel fits a trend line, how to interpret it, and when such a line is meaningful. But
since almost every student discovers this option the first time he or she makes a scatter plot,
we must mention Excel’s fitted trend line here purely as a descriptive tool that may help you
find patterns in (X, Y) data.
Exercise 6. See Section 3.7. of the textbook.
3.21 (a) Use Excel to make a scatter plot of the data for bottled water sales for 10 weeks, placing Price on
the X-axis and Units Sold on the Y-axis. Add titles and modify the default colors, fonts, etc., as you
judge appropriate to make the scatter plot effective. (b) Describe the relationship (if any) between
X and Y. Weak? Strong? Negative? Positive? Linear? Nonlinear?
WaterSold
Unit Price
Units Sold
1.15
0.94
1.04
1.05
1.08
1.33
0.99
1.25
1.16
1.11
186
216
173
182
183
150
190
165
190
201
3.22 (a) Use Excel to make a scatter plot of these vehicle data, placing Weight on the X-axis and City
MPG on the Y-axis. Add titles and modify the default colors, fonts, etc., as you judge appropriate
to make the scatter plot effective. (b) Describe the relationship (if any) between X and Y. Weak?
Strong? Negative? Positive? Linear? Nonlinear?
Weight and MPG for 20 Randomly Selected Vehicles
Vehicle
Acura TSX
BMW 3-Series
Chevrolet Corvette
Chevrolet Silverado 1500
Chrysler Pacifica
Dodge Caravan
Ford Focus
Infiniti FX
Jaguar XJ8
Lexus IS300
Lincoln Aviator
Mazda 6
Land Rover Freelander
Mercedes-Benz S-Class
Nissan 350Z
Nissan Xterra
Pontiac Vibe
Pontiac Grand Am
Toyota Sienna
Volvo C70
Random sample of 2003 vehicles.
CityMPG
City MPG
Weight (lbs.)
23
19
19
14
17
18
26
16
18
18
13
19
17
17
20
16
28
25
19
20
3,320
3,390
3,255
4,935
4,660
4,210
2,760
4,295
3,805
3,390
5,000
3,355
3,640
4,195
3,345
4,315
2,805
3,095
4,120
3,690
SECTION E