SOLUTIONS
MANUAL
TONI GARCIA
ELEMENTARY
STATISTICS
NINTH EDITION
Neil A. Weiss
Part 1: Chapter 8-14
Par 2: Chapter 1-7
All Chapters are Arranged Reverse.
, Contents
Chapter 1 The Nature of Statistics 1
Chapter 2 Organizing Data 21
Chapter 3 Descriptive Measures 125
Chapter 4 Descriptive Methods in Regression
and Correlation 213
Chapter 5 Probability and Random Variables 295
Chapter 6 The Normal Distribution 359
Chapter 7 The Sampling Distribution of the
Sample Mean 413
Chapter 8 Confidence Intervals for One
Population Mean 473
Chapter 9 Hypothesis Tests for One
Population Mean 525
Chapter 10 Inferences for Two Population Means 567
Chapter 11 Inferences for Population Proportions 627
Chapter 12 Chi-Square Procedures 661
Chapter 13 Anaylsis of Variance (ANOVA) 713
Chapter 14 Inferential Methods in Regression
and Correlation 771
,Solutions Manual Part 1: Chapter 8-14
473
CHAPTER 8 SOLUTIONS
Exercises 8.1
8.1 The value of a statistic that is used to estimate a parameter is called a
point estimate of the parameter.
8.2 A confidence-interval estimate of a parameter consists of an interval of
numbers obtained from the point estimate of the parameter together with a
‘confidence level’ that specifies how confident we are that the interval
contains the parameter. This is superior to a point estimate because it
provides some information about the accuracy of the estimate whereas a point
estimate does not.
8.3 Margin of error indicates how accurate our estimate ( x ) is an estimate for
the value of the unknown parameter ( μ ).
8.4 We can express the endpoints of the confidence interval as “point estimate”
± “margin of error”.
8.5 Approximately 95%, or 950, of the confidence intervals will contain the
value of the unknown parameter.
8.6 Approximately, 90%, or 450, of the confidence intervals will contain the
value of the unknown parameter. Therefore, 50 will not contain the value of
the unknown parameter.
_
8.7 x = 230/10 = 23.0
_
8.8 x = 110/11 = 10.0
x − ( x)
2 2
/n 6140 − (230)
8.9 s= = = 94.44 = 9.72
n −1 9
x − ( x)
2 2
/n 1530 − (110)
8.10 s= = = 43 = 6.56
n −1 10
8.11 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
20 − 2(3) / 36 to 20 + 2(3) / 36
19 to 21
(b) The margin of error is 1. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1 of our sample mean, x = 20.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 20 ± 1.
8.12 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
25 − 2(3) / 36 to 25 + 2(3) / 36
24 to 26
(b) The margin of error is 1. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1 of our sample mean, x = 25.
Copyright © 2016 Pearson Education, Inc.
, 474 Chapter 8
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 25 ± 1.
8.13 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
30 − 2(4) / 25 to 30 + 2(4) / 25
28.4 to 31.6
(b) The margin of error is 1.6. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1.6 of our sample mean, x =
30.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 30 ± 1.6.
8.14 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
35 − 2(4) / 25 to 35 + 2(4) / 25
33.4 to 36.6
(b) The margin of error is 1.6. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1.6 of our sample mean, x =
35.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 35 ± 1.6.
8.15 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
50 − 2(5) / 16 to 50 + 2(5) / 16
47.5 to 52.5
(b) The margin of error is 2.5. We can be approximately 95% confident that
the unknown parameter, μ , will be within 2.5 of our sample mean, x =
50.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 50 ± 2.5.
8.16 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
55 − 2(5) / 16 to 55 + 2(5) / 16
52.5 to 57.5
(b) The margin of error is 2.5. We can be approximately 95% confident that
the unknown parameter, μ , will be within 2.5 of our sample mean, x =
55.
Copyright © 2016 Pearson Education, Inc.
MANUAL
TONI GARCIA
ELEMENTARY
STATISTICS
NINTH EDITION
Neil A. Weiss
Part 1: Chapter 8-14
Par 2: Chapter 1-7
All Chapters are Arranged Reverse.
, Contents
Chapter 1 The Nature of Statistics 1
Chapter 2 Organizing Data 21
Chapter 3 Descriptive Measures 125
Chapter 4 Descriptive Methods in Regression
and Correlation 213
Chapter 5 Probability and Random Variables 295
Chapter 6 The Normal Distribution 359
Chapter 7 The Sampling Distribution of the
Sample Mean 413
Chapter 8 Confidence Intervals for One
Population Mean 473
Chapter 9 Hypothesis Tests for One
Population Mean 525
Chapter 10 Inferences for Two Population Means 567
Chapter 11 Inferences for Population Proportions 627
Chapter 12 Chi-Square Procedures 661
Chapter 13 Anaylsis of Variance (ANOVA) 713
Chapter 14 Inferential Methods in Regression
and Correlation 771
,Solutions Manual Part 1: Chapter 8-14
473
CHAPTER 8 SOLUTIONS
Exercises 8.1
8.1 The value of a statistic that is used to estimate a parameter is called a
point estimate of the parameter.
8.2 A confidence-interval estimate of a parameter consists of an interval of
numbers obtained from the point estimate of the parameter together with a
‘confidence level’ that specifies how confident we are that the interval
contains the parameter. This is superior to a point estimate because it
provides some information about the accuracy of the estimate whereas a point
estimate does not.
8.3 Margin of error indicates how accurate our estimate ( x ) is an estimate for
the value of the unknown parameter ( μ ).
8.4 We can express the endpoints of the confidence interval as “point estimate”
± “margin of error”.
8.5 Approximately 95%, or 950, of the confidence intervals will contain the
value of the unknown parameter.
8.6 Approximately, 90%, or 450, of the confidence intervals will contain the
value of the unknown parameter. Therefore, 50 will not contain the value of
the unknown parameter.
_
8.7 x = 230/10 = 23.0
_
8.8 x = 110/11 = 10.0
x − ( x)
2 2
/n 6140 − (230)
8.9 s= = = 94.44 = 9.72
n −1 9
x − ( x)
2 2
/n 1530 − (110)
8.10 s= = = 43 = 6.56
n −1 10
8.11 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
20 − 2(3) / 36 to 20 + 2(3) / 36
19 to 21
(b) The margin of error is 1. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1 of our sample mean, x = 20.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 20 ± 1.
8.12 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
25 − 2(3) / 36 to 25 + 2(3) / 36
24 to 26
(b) The margin of error is 1. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1 of our sample mean, x = 25.
Copyright © 2016 Pearson Education, Inc.
, 474 Chapter 8
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 25 ± 1.
8.13 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
30 − 2(4) / 25 to 30 + 2(4) / 25
28.4 to 31.6
(b) The margin of error is 1.6. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1.6 of our sample mean, x =
30.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 30 ± 1.6.
8.14 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
35 − 2(4) / 25 to 35 + 2(4) / 25
33.4 to 36.6
(b) The margin of error is 1.6. We can be approximately 95% confident that
the unknown parameter, μ , will be within 1.6 of our sample mean, x =
35.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 35 ± 1.6.
8.15 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
50 − 2(5) / 16 to 50 + 2(5) / 16
47.5 to 52.5
(b) The margin of error is 2.5. We can be approximately 95% confident that
the unknown parameter, μ , will be within 2.5 of our sample mean, x =
50.
(c) The endpoints of a confidence interval are found by
point estimate ± margin of error. For the interval in part (a), we
have 50 ± 2.5.
8.16 (a) The approximate confidence interval will be
x − 2σ / n to x + 2σ / n
55 − 2(5) / 16 to 55 + 2(5) / 16
52.5 to 57.5
(b) The margin of error is 2.5. We can be approximately 95% confident that
the unknown parameter, μ , will be within 2.5 of our sample mean, x =
55.
Copyright © 2016 Pearson Education, Inc.
