Solution Manual For
Introductory Statistics Exploring the World Through Data, Canadian Edition, 1st edition Robert
N. Gould Colleen Ryan Jim Stallard Michelle Boué
Chapters 1-14
Chapter 1: Introduction to Data
SECTION 1.2
1.1 a. The variable ―Handedness‖ is a categorical variable since its values are categories: ―Left‖ or ―Right.‖
b. The variable ―Age‖ is a numerical variable since its values are quantities.
1.2 a. The variable ―Shoe size‖ is a numerical variable since its values are quantities.
b. The variable ―Eye colour‖ is a categorical variable since its values are categories such as ―Blue‖ or
―Brown.‖
1.3 Persons who have responded that they are male have been coded with a ―1,‖ and the others are coded with a
―0.‖ Since these are categories, the variable ―Male‖ is categorical. Yes, summing the ―Male‖ categorical
variable makes sense; doing so gives the total number of persons who classified themselves as males.
1.4 We use a ―1‖ for full-time students, and for those who are not are classified as full-time, we use ―0.‖
Credits Full
5 1
4 1
1.5 0
5.5 1
6 1
3 0
2.5 0
3 0
5 1
2.5 0
4.5 1
1.5 a. The data are presented in a stacked format.
b. Smokers are indicated by ―1‖ and nonsmokers are indicated by ―0.‖
c. The table shows the data presented in an unstacked format.
Smoker Nonsmoker
15 18
14 23
13 19
23 21
18
15
,1.6 a. The data are presented in an unstacked format.
b. The table shows the data presented in a stacked format.
Age Class
31 5 p.m.
34 5 p.m.
46 5 p.m.
47 5 p.m.
50 5 p.m.
24 Noon
18 Noon
21 Noon
20 Noon
20 Noon
SECTION 1.3
1.7 a. The percentage of answers that were changed for the students told not to change is found by dividing
the number of students who changed by the total number of students who were told not to change. This
189
gives 0.00638 or approximately 0.64%.
29617
b. The percentage of answers that were changed for the students told to change is found by dividing the
number of students who changed by the total number of students who were told not to change. This
124
gives 0.00854 or approximately 0.85%.
14513
c. The higher percentage of students who changed is found in the class that was told to change their
answers if they felt they had found a better answer, so it appears that perhaps the instruction to do so
had a measurable effect. Since both percentages are less than 1%, the effect would be very small.
1.8 a. For the class that was instructed not to change, a total of 189 students changed their answers. The
91
percentage of changes made from wrong to right is therefore 0.481 or approximately 48.1%.
189
48
The percentage of changes made from right to wrong is 0.254 or 25.4%. Since more students
189
changed from wrong to right, then on average, their grades improved.
b. For the class that was instructed to change, a total of 124 students changed their answers. The
86
percentage of changes made from wrong to right is then 0.694 or 69.4%. The percentage of
124
24
changes made from right to wrong is 0.194 or 19.4%. Since more students changed from wrong
124
to right, then on average, their grades improved.
c. It is better to change your answer if you believe the second one you found is more reasonable.
, 15
1.9 a. 0.395 or 39.5%.
This statistics class has a total of 38 students, so the percentage that is male is
38
b. 64.1% of 234 can be calculated by 0.641 234 149.994 . Therefore, 150 members of the class are
men.
c. This time the class size is unknown; call it C. Then 40% of C is 20, or in symbols:
0.40 C 20 or equivalently C 20 50.
0.4
1.10 a. The percentage of RNs employed in nursing who were male is 17,163 0.0639 or 6.4%.
268,512
b. The percentage or RNs employed in nursing who were educated in Canada is 100 8.6 91.4%.
Therefore, the number of RNs employed in nursing who were educated in Canada is 91.4% of 268,512.
Calculate this by 0.914 × 268,512 245,420 RNs.
c. The total number RNs employed in direct patient care nursing is unknown; let’s call it T. Then we
know that 7.5% of T is 17,645. In symbols, this is 0.075T 17,645 or that
T 17 ,645 235 ,267 RNs were employed in direct patient care nursing.
0.075
1.11 The frequency of women is seven. The proportion of women is 7 and the percentage is approximately
11
63.6%.
1.12 The frequency of right-handed people is nine. The proportion who are right-handed is 9 or approximately
11
81.8%.
1.13 If we let T represent the total projected population of Canada in 2061, then we know that 25.43% of T is
13,386,000. In symbols we have
0.2543 T 13,386, 000, or equivalently T 13,386,000
0.2543
52, 638, 616
Thus, the total population of Canada in 2061 is projected to be 52,638,616 people. You may round this
answer.
1.14 If we let T represent the total number of Canadians aged 12 and over in 2012, then we are told that 85.1%
of T is 25,087,068. In symbols we have
0.851 T 25, 087, 068 or equivalently T 25,087,0
0.851
68
29, 479,515.9
Rounding up gives 29,479,516 Canadians aged 12 and over. You may round this answer.
1.15 Divide the number of persons with diabetes in each province by that province’s population and add it to the
table. For example, for the province of Ontario, compute 770, 410 0.067 . Then the rate of
11, 498,657
diabetes per thousand is 0.067 1000 67. The other calculations are made similarly. The table shows the
resulting data values.
Province Persons Population Rank by Diabetes/Population Diabetes Rank by
with Diabetes Cases per 1000 Rate
Population
Ontario 770,410 11,498,657 1 0.067 67 2
Quebec 448,122 6,894,185 2 0.065 65 3
British Columbia 224,775 3,943,421 3 0.057 57 6
Alberta 195,440 3,203,934 4 0.061 61 5
Nova Scotia 69,721 810,698 5 0.086 86 1
Manitoba 62,058 1,000,935 6 0.062 62 4
, The rankings based on the rate of diabetes are different from the rankings based on the number of persons
with diabetes. For example, Nova Scotia is fifth in number of cases but it has the highest rate among these
provinces.
Among these six provinces, you would be most likely to meet someone with diabetes if you were in Nova
Scotia and least likely if you were in British Columbia.
1.16 a. Calculate the population density by dividing the population in each province by the total area of that
province. For example, to find the population density of Ontario, compute 13,678,740 12.71.
1,076,395
The other calculations are made similarly. The table shows the resulting data values.
Province Population Area Population Rank by
Density Density
Ontario 13,678,740 1,076,395 12.71 1
Quebec 8,214,672 1,542,056 5.33 3
British Columbia 4,631,302 944,735 4.90 4
Alberta 4,121,692 661,848 6.23 2
Manitoba 1,282,043 647,797 1.98 5
Saskatchewan 1,125,410 651,036 1.73 6
b. To live in the province (of these six) with lowest population density, one would choose to live in
Saskatchewan.
c. To live in the province (of these six) with highest population density, one would choose to live in
Ontario.
1.17 Compute the percentage as the number of people exposed to second-hand smoke divided by the total
population in Canada in that age group in each year and multiply by 100. For example, the percentage of
people exposed to second-hand smoke in 2003 is
2,148
20,264
100 10.6%. The table shows the resulting data
values.
Year Exposed Total Percentage
2003 2,148 20,264 10.6
2005 1,847 20,987 8.8
2007 1,600 21,621 7.4
2009 1,417 22,855 6.2
2011 1,268 23,055 5.5
The percentage of people exposed to second-hand smoke is decreasing over time.
1.18 Compute the percentage of elderly as the number of elderly people divided by the total population of
1.8
Canada and multiply by 100. For example, the percentage of elderly people in 1972 is 100 8.1%.
22.2
The table shows the resulting values.
Year Elderly Population Percentage
1972 1.8 22.2 8.1
1982 2.4 25.1 9.6
1992 3.3 28.4 11.6
Introductory Statistics Exploring the World Through Data, Canadian Edition, 1st edition Robert
N. Gould Colleen Ryan Jim Stallard Michelle Boué
Chapters 1-14
Chapter 1: Introduction to Data
SECTION 1.2
1.1 a. The variable ―Handedness‖ is a categorical variable since its values are categories: ―Left‖ or ―Right.‖
b. The variable ―Age‖ is a numerical variable since its values are quantities.
1.2 a. The variable ―Shoe size‖ is a numerical variable since its values are quantities.
b. The variable ―Eye colour‖ is a categorical variable since its values are categories such as ―Blue‖ or
―Brown.‖
1.3 Persons who have responded that they are male have been coded with a ―1,‖ and the others are coded with a
―0.‖ Since these are categories, the variable ―Male‖ is categorical. Yes, summing the ―Male‖ categorical
variable makes sense; doing so gives the total number of persons who classified themselves as males.
1.4 We use a ―1‖ for full-time students, and for those who are not are classified as full-time, we use ―0.‖
Credits Full
5 1
4 1
1.5 0
5.5 1
6 1
3 0
2.5 0
3 0
5 1
2.5 0
4.5 1
1.5 a. The data are presented in a stacked format.
b. Smokers are indicated by ―1‖ and nonsmokers are indicated by ―0.‖
c. The table shows the data presented in an unstacked format.
Smoker Nonsmoker
15 18
14 23
13 19
23 21
18
15
,1.6 a. The data are presented in an unstacked format.
b. The table shows the data presented in a stacked format.
Age Class
31 5 p.m.
34 5 p.m.
46 5 p.m.
47 5 p.m.
50 5 p.m.
24 Noon
18 Noon
21 Noon
20 Noon
20 Noon
SECTION 1.3
1.7 a. The percentage of answers that were changed for the students told not to change is found by dividing
the number of students who changed by the total number of students who were told not to change. This
189
gives 0.00638 or approximately 0.64%.
29617
b. The percentage of answers that were changed for the students told to change is found by dividing the
number of students who changed by the total number of students who were told not to change. This
124
gives 0.00854 or approximately 0.85%.
14513
c. The higher percentage of students who changed is found in the class that was told to change their
answers if they felt they had found a better answer, so it appears that perhaps the instruction to do so
had a measurable effect. Since both percentages are less than 1%, the effect would be very small.
1.8 a. For the class that was instructed not to change, a total of 189 students changed their answers. The
91
percentage of changes made from wrong to right is therefore 0.481 or approximately 48.1%.
189
48
The percentage of changes made from right to wrong is 0.254 or 25.4%. Since more students
189
changed from wrong to right, then on average, their grades improved.
b. For the class that was instructed to change, a total of 124 students changed their answers. The
86
percentage of changes made from wrong to right is then 0.694 or 69.4%. The percentage of
124
24
changes made from right to wrong is 0.194 or 19.4%. Since more students changed from wrong
124
to right, then on average, their grades improved.
c. It is better to change your answer if you believe the second one you found is more reasonable.
, 15
1.9 a. 0.395 or 39.5%.
This statistics class has a total of 38 students, so the percentage that is male is
38
b. 64.1% of 234 can be calculated by 0.641 234 149.994 . Therefore, 150 members of the class are
men.
c. This time the class size is unknown; call it C. Then 40% of C is 20, or in symbols:
0.40 C 20 or equivalently C 20 50.
0.4
1.10 a. The percentage of RNs employed in nursing who were male is 17,163 0.0639 or 6.4%.
268,512
b. The percentage or RNs employed in nursing who were educated in Canada is 100 8.6 91.4%.
Therefore, the number of RNs employed in nursing who were educated in Canada is 91.4% of 268,512.
Calculate this by 0.914 × 268,512 245,420 RNs.
c. The total number RNs employed in direct patient care nursing is unknown; let’s call it T. Then we
know that 7.5% of T is 17,645. In symbols, this is 0.075T 17,645 or that
T 17 ,645 235 ,267 RNs were employed in direct patient care nursing.
0.075
1.11 The frequency of women is seven. The proportion of women is 7 and the percentage is approximately
11
63.6%.
1.12 The frequency of right-handed people is nine. The proportion who are right-handed is 9 or approximately
11
81.8%.
1.13 If we let T represent the total projected population of Canada in 2061, then we know that 25.43% of T is
13,386,000. In symbols we have
0.2543 T 13,386, 000, or equivalently T 13,386,000
0.2543
52, 638, 616
Thus, the total population of Canada in 2061 is projected to be 52,638,616 people. You may round this
answer.
1.14 If we let T represent the total number of Canadians aged 12 and over in 2012, then we are told that 85.1%
of T is 25,087,068. In symbols we have
0.851 T 25, 087, 068 or equivalently T 25,087,0
0.851
68
29, 479,515.9
Rounding up gives 29,479,516 Canadians aged 12 and over. You may round this answer.
1.15 Divide the number of persons with diabetes in each province by that province’s population and add it to the
table. For example, for the province of Ontario, compute 770, 410 0.067 . Then the rate of
11, 498,657
diabetes per thousand is 0.067 1000 67. The other calculations are made similarly. The table shows the
resulting data values.
Province Persons Population Rank by Diabetes/Population Diabetes Rank by
with Diabetes Cases per 1000 Rate
Population
Ontario 770,410 11,498,657 1 0.067 67 2
Quebec 448,122 6,894,185 2 0.065 65 3
British Columbia 224,775 3,943,421 3 0.057 57 6
Alberta 195,440 3,203,934 4 0.061 61 5
Nova Scotia 69,721 810,698 5 0.086 86 1
Manitoba 62,058 1,000,935 6 0.062 62 4
, The rankings based on the rate of diabetes are different from the rankings based on the number of persons
with diabetes. For example, Nova Scotia is fifth in number of cases but it has the highest rate among these
provinces.
Among these six provinces, you would be most likely to meet someone with diabetes if you were in Nova
Scotia and least likely if you were in British Columbia.
1.16 a. Calculate the population density by dividing the population in each province by the total area of that
province. For example, to find the population density of Ontario, compute 13,678,740 12.71.
1,076,395
The other calculations are made similarly. The table shows the resulting data values.
Province Population Area Population Rank by
Density Density
Ontario 13,678,740 1,076,395 12.71 1
Quebec 8,214,672 1,542,056 5.33 3
British Columbia 4,631,302 944,735 4.90 4
Alberta 4,121,692 661,848 6.23 2
Manitoba 1,282,043 647,797 1.98 5
Saskatchewan 1,125,410 651,036 1.73 6
b. To live in the province (of these six) with lowest population density, one would choose to live in
Saskatchewan.
c. To live in the province (of these six) with highest population density, one would choose to live in
Ontario.
1.17 Compute the percentage as the number of people exposed to second-hand smoke divided by the total
population in Canada in that age group in each year and multiply by 100. For example, the percentage of
people exposed to second-hand smoke in 2003 is
2,148
20,264
100 10.6%. The table shows the resulting data
values.
Year Exposed Total Percentage
2003 2,148 20,264 10.6
2005 1,847 20,987 8.8
2007 1,600 21,621 7.4
2009 1,417 22,855 6.2
2011 1,268 23,055 5.5
The percentage of people exposed to second-hand smoke is decreasing over time.
1.18 Compute the percentage of elderly as the number of elderly people divided by the total population of
1.8
Canada and multiply by 100. For example, the percentage of elderly people in 1972 is 100 8.1%.
22.2
The table shows the resulting values.
Year Elderly Population Percentage
1972 1.8 22.2 8.1
1982 2.4 25.1 9.6
1992 3.3 28.4 11.6
