SECTION 1.1 1
Chapter 1
Section 1.1
1. (a) The population consists of all the times the process could be run. It is conceptual.
(b) The population consist of all the registered voters in the state. It is tangible.
(c) The population consist of all people with high cholesterol levels. It is tangible.
(d) The population consist of all concrete specimens that could be made from the new formulation. It is conceptual.
(e) The population consist of all bolts manufactured that day. It is tangible.
2. (iii). It is very unlikely that students whose names happen to fall at the top of a page in the phone book will differ
systematically in height from the population of students as a whole. It is somewhat more likely that engineering
majors will differ, and very likely that students involved with basketball intramurals will differ.
3. (a) False
(b) True
4. (a) False
(b) True
5. (a) No. What is important is the population proportion of defectives; the sample proportion is only an approxima-
tion. The population proportion for the new process may in fact be greater or less than that of the old process.
(b) No. The population proportion for the new process may be 0.12 or more, even though the sample proportion
was only 0.11.
(c) Finding 2 defective circuits in the sample.
6. (a) False
Page 1
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
,2 CHAPTER 1
(b) True
(c) True
7. A good knowledge of the process that generated the data.
8. (a) An observational study
(b) It is not well-justified. Because the study is observational, there could be differences between the groups other
than the level of exercise. These other differences (confounders) could cause the difference in blood pressure.
9. (a) A controlled experiment
(b) It is well-justified, because it is based on a controlled experiment rather than an observational study.
Section 1.2
1. False
2. No. In the sample 1, 2, 4, the mean is 7/3, which does not appear at all.
3. No. In the sample 1, 2, 4, the mean is 7/3, which does not appear at all.
4. No. The median of the sample 1, 2, 4, 5 is 3.
5. The sample size can be any odd number.
Page 2
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
, SECTION 1.2 3
6. Yes. For example, the list 1, 2, 12 has an average of 5 and a standard deviation of 6.08.
7. Yes. If all the numbers in the list are the same, the standard deviation will equal 0.
8. The mean increases by $50; the standard deviation is unchanged.
9. The mean and standard deviation both increase by 5%.
10. (a) Let 𝑋1 , ..., 𝑋100 denote the 100 numbers of occupants.
∑
100
𝑋𝑖 = 70(1) + 15(2) + 10(3) + 3(4) + 2(5) = 152
𝑖=1
∑100
𝑖=1 𝑋𝑖 152
𝑋= = = 1.52
100 100
(b) The sample variance is
( 100 )
1 ∑ 2
𝑠2 = 𝑋 − 100𝑋
2
99 𝑖=1 𝑖
1
= [(70)12 + (15)22 + (10)32 + (3)42 + (2)52 − 100(1.522 )]
99
= 0.87838
√
The standard deviation is 𝑠 = 𝑠2 = 0.9372.
Alternatively, the sample variance can be computed as
1 ∑
100
𝑠2 = (𝑋 − 𝑋)2
99 𝑖=1 𝑖
1
= [70(1 − 1.52)2 + 15(2 − 1.52)2 + 10(3 − 1.52)2 + 3(4 − 1.52)2 + 2(5 − 1.52)2 ]
99
= 0.87838
(c) The sample median is the average of the 50th and 51st value when arranged in order. Both these values are
equal to 1, so the median is 1.
Page 3
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
Chapter 1
Section 1.1
1. (a) The population consists of all the times the process could be run. It is conceptual.
(b) The population consist of all the registered voters in the state. It is tangible.
(c) The population consist of all people with high cholesterol levels. It is tangible.
(d) The population consist of all concrete specimens that could be made from the new formulation. It is conceptual.
(e) The population consist of all bolts manufactured that day. It is tangible.
2. (iii). It is very unlikely that students whose names happen to fall at the top of a page in the phone book will differ
systematically in height from the population of students as a whole. It is somewhat more likely that engineering
majors will differ, and very likely that students involved with basketball intramurals will differ.
3. (a) False
(b) True
4. (a) False
(b) True
5. (a) No. What is important is the population proportion of defectives; the sample proportion is only an approxima-
tion. The population proportion for the new process may in fact be greater or less than that of the old process.
(b) No. The population proportion for the new process may be 0.12 or more, even though the sample proportion
was only 0.11.
(c) Finding 2 defective circuits in the sample.
6. (a) False
Page 1
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
,2 CHAPTER 1
(b) True
(c) True
7. A good knowledge of the process that generated the data.
8. (a) An observational study
(b) It is not well-justified. Because the study is observational, there could be differences between the groups other
than the level of exercise. These other differences (confounders) could cause the difference in blood pressure.
9. (a) A controlled experiment
(b) It is well-justified, because it is based on a controlled experiment rather than an observational study.
Section 1.2
1. False
2. No. In the sample 1, 2, 4, the mean is 7/3, which does not appear at all.
3. No. In the sample 1, 2, 4, the mean is 7/3, which does not appear at all.
4. No. The median of the sample 1, 2, 4, 5 is 3.
5. The sample size can be any odd number.
Page 2
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
, SECTION 1.2 3
6. Yes. For example, the list 1, 2, 12 has an average of 5 and a standard deviation of 6.08.
7. Yes. If all the numbers in the list are the same, the standard deviation will equal 0.
8. The mean increases by $50; the standard deviation is unchanged.
9. The mean and standard deviation both increase by 5%.
10. (a) Let 𝑋1 , ..., 𝑋100 denote the 100 numbers of occupants.
∑
100
𝑋𝑖 = 70(1) + 15(2) + 10(3) + 3(4) + 2(5) = 152
𝑖=1
∑100
𝑖=1 𝑋𝑖 152
𝑋= = = 1.52
100 100
(b) The sample variance is
( 100 )
1 ∑ 2
𝑠2 = 𝑋 − 100𝑋
2
99 𝑖=1 𝑖
1
= [(70)12 + (15)22 + (10)32 + (3)42 + (2)52 − 100(1.522 )]
99
= 0.87838
√
The standard deviation is 𝑠 = 𝑠2 = 0.9372.
Alternatively, the sample variance can be computed as
1 ∑
100
𝑠2 = (𝑋 − 𝑋)2
99 𝑖=1 𝑖
1
= [70(1 − 1.52)2 + 15(2 − 1.52)2 + 10(3 − 1.52)2 + 3(4 − 1.52)2 + 2(5 − 1.52)2 ]
99
= 0.87838
(c) The sample median is the average of the 50th and 51st value when arranged in order. Both these values are
equal to 1, so the median is 1.
Page 3
PROPRIETARY MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual
may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of
the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their
individual course preparation. If you are a student using this Manual, you are using it without permission.
