Chapter One
1.1
The word ‘statistics’ has the following two meanings:
i.
First, it refers to numerical facts such as the ages of persons, incomes of families, etc.
ii.
Second, it refers to the field of study. It provides us with techniques that help us to collect,
analyze, present, and interpret data and to make decisions.
1.3
Population: All elements whose characteristics are being studied.
Sample: A portion of the population selected for a study.
Representative sample: A sample that possesses the characteristics of the population as closely as
possible.
Random sample: A sample drawn in such a way that each element of the population has some chance
of being included in the sample.
Sampling with replacement: A sampling procedure in which the item selected at each selection is put
back in the population before the next item is drawn.
Sampling without replacement: A sampling procedure in which the item selected at each selection is
not replaced in the population.
1.5
A census is a survey that includes all members of the population. A survey based on a portion of the
population is called a sample survey. A sample survey is preferred over a census for the following
reasons:
i.
Conducting a census is very expensive because the size of the population is usually very large.
ii.
Conducting a census is very time consuming.
1
2
Chapter One
iii. In many cases it is almost impossible to identify every member of the target population.
1.7
a. Population
b. Sample
c. Population
1.9
Member: Each city included in the table.
d. Sample
e. Population
Variable: Number of dog bites reported.
Measurement: Dog bites in a specific city. For example, Oakdale’s 12 dog bites is a measurement.
Data set: Collection of dog bite numbers for the six cities listed in the table.
1.11
a.
Dog Bites
b. Six observations
c. Six elements (cities)
1.13
a.
Quantitative variable: A variable that can assume numerical values.
b.
Qualitative variable: A variable that cannot be measured numerically but can be divided into
different categories.
c.
Discrete variable: A variable whose values are countable.
d.
Continuous variable: A variable that can assume any value over a certain interval or intervals.
e.
Quantitative data: Data collected on a quantitative variable.
f.
Qualitative data: Data collected on a qualitative variable.
1.15
a. Quantitative
b. Quantitative
c. Qualitative
d. Quantitative
e. Quantitative
1.17
a. Discrete
b. Continuous
d. Discrete
e. Continuous
1.19
Excel: In the first column type in Name and press ENTER, type in JACK and press ENTER, and repeat
until all five names are listed. Then use the arrow keys or the mouse to move to the top of the second
column. Type in Height(cm) and press ENTER, type in 165 and press ENTER, and repeat until all of
the numbers are listed.
Mann - Introductory Statistics, Fifth Edition, Students Solutions Manual
3
Note: To format the table like the textbook: Highlight the tops row and right click the mouse, selecting format cells,
near the top of the pop up box select Borders. Then about a third of the way down on the left side of the box it says
Border, under the word Border click on the box with the dark line on top of the box and then click on the box with
the dark line on the bottom of the box. And then click on OK. To put in the line at the bottom of the table repeat
these steps but do not click on the box with the dark line on top – just the one with the dark line on the bottom.
MINITAB Type the labels Name and Height (cm) in the grey row between the down arrow and 1. In the
first row type Jack and press ENTER and repeat for all of the other names in the list. Use the mouse or
the right arrow to move top of the second column. Enter each number and press ENTER.
1.21 Internal sources of data are a company’s own files and records.
External sources of data are the sources that do not belong to a company.
1.23 a.
Cross-section data
b. Cross-section data
c. Time-series data
1.25
m
3
6
25
12
15
18
Sum= 79
a.  f = 69
f
16
11
16
8
4
14
69
b. m2 = 1363
M2
9
36
625
144
225
324
1363
Mf
48
66
400
96
60
252
992
c.  mf = 992
m2 f
144
396
10,000
1152
900
4536
17,128
d.  m 2 f= 17,128
d. Time-series data
4
Chapter One
TI-83: Insert numbers as two lisst and then do the calculations as follows: press the 2 nd key, then
STAT, use the arrows to move over to MATH, use the arrows to move down to 5 sum or by pressing
the number 5 key, and press ENTER. To sum the list in column L1 next press the 2nd key, the number
1 key, and then entering ) followed by ENTER. If you wish to sum the list in the second column do all
of the above except this time press the number 2 key instead of the number 1 key. To do additional
math before the summation just include the multiplication or press the key to square a number before
entering the right parenthesis. The results here look only slightly different than those shown above.
Sum (L1)
Sum (L1 * L2)
79
Sum (L2)
992
Sum (L1 2 * L2 )
69
17128
Sum (L1 2)
1363
MINITAB: Enter the data for m and f into columns C1 and C2 with the labels m and f in the gray row
just below the column numbers. Now select Calc and then Column Statistics causing a pop-up-box to
open. Under the word Statistic is Sum and click on the box to the left of it and in the space beside the
words Input variable type in the column to be added up which in this case is m. To sum the squares
instead of clicking beside the word sum, this time click to the left of the words Sum of Squares which
is near the top of the second column and in the box replace m with f.
To calculate Σmf select Calc and then Calculator which brings up the pop-up-box. Under the word
“Expression” type in C1* C2 and in the box beside “store result in variable” type C3. Label this
column mf. Do the same for Σm2f except type the expression as C1*C1*C2 its stored in C4, and
labeled mmf. Then total the columns as you did for m and f.
Mann - Introductory Statistics, Fifth Edition, Students Solutions Manual
5
Excel: Enter the data in two columns and at the top of each column be sure to label them. In an empty
cell type =SUM(cell names) and press ENTER. Here I used column c for f so its =SUM(c2:c7) and
ENTER. To get the sum of the squares for m, insert the formula =SUMSQ(cell range) which in this
example is =SUMSQ(B2:B7). To calculate the sum of the product of m*f enter the formula
=SUMPRODUCT(cell range 1,cell range 2) and in this example it becomes
=SUMPRODUCT(B2:B7,C2:C7). To get the sum of m2f enter the formula =SUMPRODUCT(cell
range 1, cell range 1, cell range 2) which in this example is =SUMPRODUCT(B2:B7,B2:B7,C2:C7).
Note that all of these formulas can be found by selecting Insert, Function, and scrolling down until the
function name appears in the box. Then all you need to do is enter the appropriate cell ranges. The
second image here, presents the results when following the instruction on page 24 of the textbook
which are slightly different than those presented here.
1.27
x
4
18
25
9
12
20
x = 88
a. x = 88
1.29
y
12
5
14
7
12
8
y =58
b. y =58
xy
48
90
350
63
144
160
xy = 855
x2
16
324
625
81
144
400
x2 = 1590
c. xy = 855
y2
144
25
196
49
144
64
y2 = 622
d. x2 = 1590
a. y = 83 + 205 + 57 + 134 = $479
e. y2 = 622
b. (y)2 = (479)2 = 229,441
c.  y2= (83)2 + (205)2 + (57)2 + (134)2 = 70,119
1.31
a. x= 7 + 39 + 21 + 16 + 3 + 43 + 19 = 148 students
b. (x)2 = (148) 2 = 21,904
c.  x2= (7)2 + (39) 2 + (21)2 + (16)2 + (3)2 + (43)2 + (19) 2 = 4486 students
1.33
Variable: The number of U.S. babies born as triplets and larger sets.
6
Chapter One
Measurement: The number of U.S. babies born as triplets and larger sets for a specific year.
Data Set: Collection of the number of U.S. babies born as triplets and larger sets for the years listed in
the table.
1.35
a.
Sample
b. Population for the year
c. Sample
d. Population
1.37
a.
Sampling without replacement, because once a patient is selected, he/she will not be replaced
before the next patient is selected. All 10 selected patients must be different.
b.
Sampling with replacement because both times the selection is made from the same group
(consisting of all professors).
1.39
a.
 x = 8 + 14 + 3 + 7 + 10 + 5= 47 shoe pairs
c.
 x2 = (8) 2 + (14) 2 + (3) 2 + (7) 2 + (10) 2 + (5) 2 = 443 shoes
b. (x)2 = (47)2 = 2209
1.41
m
3
16
11
9
20
Sum= 59
a.  m = 59
f
7
32
17
12
34
102
f2
49
1024
289
144
1156
2662
b.  f 2 = 2662
m2f
63
8192
2057
972
13,600
24,884
mf
21
512
187
108
680
1508
c.  mf = 1508
m2
9
256
121
81
400
867
d.  m2f = 24,884
e.  m2 = 867
Self-Review Test for Chapter One
1.
b
2.
c
3.
a. A sample without replacement
b. A sample with replacement
4.
a. Qualitative
5.
Member: A specific job included in the table. For example, Coach is a member.
b. Quantitative; continuous c. Quantitative; discrete
Variable: Votes for the best job at the Superbowl.
d. Quantitative; continuous
Mann - Introductory Statistics, Fifth Edition, Students Solutions Manual
7
Measurement: Votes for a specific Superbowl job. For example, Coach received 1,927 votes is a
measurement.
Data set: The collection of votes for the five Superbowl jobs listed in the table.
6.
a.
 x = 8 + 5 + 10 + 6 + 5 + 8 = 42 rooms
c.
 x2 = (8)2 + (5)2 + (10)2 + (6)2 + (5)2 + (8)2 = 314
b. (x)2 = (42)2 =1764
7.
m
3
6
9
12
15
m = 45
f
15
25
40
20
12
f = 112
a. m = 45 b.  f = 112
m2
9
36
81
144
225
m2 = 495
c.  m2 = 495
mf
45
150
360
240
180
mf = 975
m2f
135
900
3240
2880
2700
m2f = 9855
d.  mf = 975
f2
225
625
1600
400
144
f 2 = 2994
e. m2f = 9855
f.  f2 = 2994
8
Chapter One