Mathematical Statistics with Applications in R, Third Edition [3rd Ed] (Instructor's Solution Manual) (Solutions)

Cover
Mathematical Statistics with Applications in R
Copyright
Dedication
Acknowledgments
About the authors
Preface
	Preface to the Third Edition
	Preface to the Second Edition
	Preface to the First Edition
	Aim and Objective of the Textbook
	Features
Flow chart
1. Descriptive statistics
	1.1 Introduction
		1.1.1 Data collection
	1.2 Basic concepts
		1.2.1 Types of data
	Exercises 1.2
	1.3 Sampling schemes
		1.3.1 Errors in sample data
		1.3.2 Sample size
	Exercises 1.3
	1.4 Graphical representation of data
	Exercises 1.4
	1.5 Numerical description of data
		1.5.1 Numerical measures for grouped data
		1.5.2 Box plots
	Exercises 1.5
	1.6 Computers and statistics
	1.7 Chapter summary
	1.8 Computer examples
		1.8.1 R introduction and examples
			Importing a CSV file
			Exporting a CSV
		1.8.2 Minitab examples
		1.8.3 SPSS examples
		1.8.4 SAS examples
	Exercises 1.8
	Projects for chapter 1
		1A World Wide Web and data collection
		1B Preparing a list of useful Internet sites
		1C Dot plots and descriptive statistics
		1D Importance of statistics in our society
		1E Uses and misuses of statistics
2. Basic concepts from probability theory
	2.1 Introduction
	2.2 Random events and probability
	Exercises 2.2
	2.3 Counting techniques and calculation of probabilities
	Exercises 2.3
	2.4 The conditional probability, independence, and Bayes' rule
	Exercises 2.4
	2.5 Random variables and probability distributions
	Exercises 2.5
	2.6 Moments and moment-generating functions
		2.6.1 Skewness and kurtosis
	Exercises 2.6
	2.7 Chapter summary
	2.8 Computer examples (optional)
		2.8.1 Examples using R
		2.8.2 Minitab computations
		2.8.3 SPSS examples
		2.8.4 SAS examples
	Projects for chapter 2
		2A The birthday problem
		2B The Hardy-Weinberg law
		2C Some basic probability simulation
3. Additional topics in probability
	3.1 Introduction
	3.2 Special distribution functions
		3.2.1 The binomial probability distribution
		3.2.2 Poisson probability distribution
		3.2.3 Uniform probability distribution
		3.2.4 Normal probability distribution
		3.2.5 Gamma probability distribution
	Exercises 3.2
	3.3 Joint probability distributions
		3.3.1 Covariance and correlation
	Exercises 3.3
	3.4 Functions of random variables
		3.4.1 Method of distribution functions
		3.4.2 The probability density function of Y = g(X), where g is differentiable and monotone increasing or decreasing
		3.4.3 Probability integral transformation
		3.4.4 Functions of several random variables: method of distribution functions
		3.4.5 Transformation method
	Exercises 3.4
	3.5 Limit theorems
	Exercises 3.5
	3.6 Chapter summary
	3.7 Computer examples (optional)
		3.7.1 The R examples
		3.7.2 Minitab examples
		3.7.3 Distribution checking
		3.7.4 SPSS examples
		3.7.5 SAS examples
	Projects for Chapter 3
		3A Mixture distribution
		3B Generating samples from exponential and Poisson probability distribution
	Exercise 3B
		3C Coupon collector's problem
		3D Recursive calculation of binomial and Poisson probabilities
		3E Simulation of Poisson approximation of binomial
		3F Generating a large amount of random data using R
4. Sampling distributions
	4.1 Introduction
		4.1.1 Finite populations
	Exercises 4.1
	4.2 Sampling distributions associated with normal populations
		4.2.1 Chi-square distribution
		4.2.2 Student t distribution
		4.2.3 F-distribution
	Exercises 4.2
	4.3 Order statistics
	Exercises 4.3
	4.4 The normal approximation to the binomial distribution
	Exercises 4.4
	4.5 Chapter summary
	4.6 Computer examples
		4.6.1 Examples using R
		4.6.2 Minitab examples
		4.6.3 SPSS examples
		4.6.4 SAS examples
	Projects for chapter 4
		4A A method to obtain random samples from different distributions
		4B Simulation experiments
		4C A test for normality
	Exercises
5. Statistical estimation
	5.1 Introduction
	5.2 The methods of finding point estimators
		5.2.1 The method of moments
		5.2.2 The method of maximum likelihood
			5.2.2.1 Some additional probability distributions
	Exercises 5.2
	5.3 Some desirable properties of point estimators
		5.3.1 Unbiased estimators
		5.3.2 Sufficiency
	Exercises 5.3
	5.4 A method of finding the confidence interval: pivotal method
	Exercises 5.4
	5.5 One-sample confidence intervals
		5.5.1 Large-sample confidence intervals
		5.5.2 Confidence interval for proportion, p
			5.5.2.1 Margin of error and sample size
		5.5.3 Small-sample confidence intervals for μ
	Exercises 5.5
	5.6 A confidence interval for the population variance
	Exercises 5.6
	5.7 Confidence interval concerning two population parameters
	Exercises 5.7
	5.8 Chapter summary
	5.9 Computer examples
		5.9.1 Examples using R
		5.9.2 Minitab examples
		5.9.3 SPSS examples
		5.9.4 SAS examples
	Exercises 5.9
	5.10 Projects for Chapter 5
		5.10.1 Asymptotic properties
		5.10.2 Robust estimation
		5.10.3 Numerical unbiasedness and consistency
		5.10.4 Averaged squared errors
		5.10.5 Alternate method of estimating the mean and variance
		5.10.6 Newton-Raphson in one dimension
		5.10.7 The empirical distribution function
		5.10.8 Simulation of coverage of the small confidence intervals for μ
		5.10.9 Confidence intervals based on sampling distributions
		5.10.10 Large-sample confidence intervals: general case
		5.10.11 Prediction interval for an observation from a normal population
		5.10.12 Empirical distribution function as estimator for cumulative distribution function
6. Hypothesis testing
	6.1 Introduction
		6.1.1 Sample size
	Exercises 6.1
	6.2 The Neyman-Pearson lemma
	Exercises 6.2
	6.3 Likelihood ratio tests
	Exercises 6.3
	6.4 Hypotheses for a single parameter
		6.4.1 The p value
		6.4.2 Hypothesis testing for a single parameter
	Exercises 6.4
	6.5 Testing of hypotheses for two samples
		6.5.1 Independent samples
			6.5.1.1 Equal variances
			6.5.1.2 Unequal variances: Welch's t-test (σ12≠σ22)
		6.5.2 Dependent samples
	Exercises 6.5
	6.6 Chapter summary
	6.7 Computer examples
		6.7.1 R examples
		6.7.2 Minitab examples
		6.7.3 SPSS examples
		6.7.4 SAS examples
	Projects for Chapter 6
		6A Testing on computer-generated samples
		6B Conducting a statistical test with confidence interval
7. Linear regression models
	7.1 Introduction
	7.2 The simple linear regression model
		7.2.1 The method of least squares
		7.2.2 Derivation of β^0 and β^1
		7.2.3 Quality of the regression
		7.2.4 Properties of the least-squares estimators for the model Y=β0 + β1x + ε
		7.2.5 Estimation of error variance σ2
	Exercises 7.2
	7.3 Inferences on the least-squares estimators
		7.3.1 Analysis of variance approach to regression
	Exercises 7.3
	7.4 Predicting a particular value of Y
	Exercises 7.4
	7.5 Correlation analysis
	Exercises 7.5
	7.6 Matrix notation for linear regression
		7.6.1 ANOVA for multiple regression
	Exercises 7.6
	7.7 Regression diagnostics
	7.8 Chapter summary
	7.9 Computer examples
		7.9.1 Examples using R
		7.9.2 Minitab examples
		7.9.3 SPSS examples
		7.9.4 SAS examples
	Projects for chapter 7
		7A Checking the adequacy of the model by scatterplots
		7B The coefficient of determination
		7C Outliers and high leverage points
8. Design of experiments
	8.1 Introduction
	8.2 Concepts from experimental design
		8.2.1 Basic terminology
		8.2.2 Fundamental principles: replication, randomization, and blocking
		8.2.3 Some specific designs
	Exercises 8.2
	8.3 Factorial design
		8.3.1 One-factor-at-a-time design
		8.3.2 Full factorial design
		8.3.3 Fractional factorial design
	Exercises 8.3
	8.4 Optimal design
		8.4.1 Choice of optimal sample size
	Exercises 8.4
	8.5 The Taguchi methods
	Exercises 8.5
	8.6 Chapter summary
	8.7 Computer examples
		8.7.1 Examples using R
		8.7.2 Minitab examples
		8.7.3 SAS examples
	Projects for chapter 8
		8A Sample size and power
		8B Effect of temperature on the spoilage of milk
9. Analysis of variance
	9.1 Introduction
	9.2 Analysis of variance method for two treatments (optional)
	Exercises 9.2
	9.3 Analysis of variance for a completely randomized design
		9.3.1 The p-value approach
		9.3.2 Testing the assumptions for one-way analysis of variance
		9.3.3 Model for one-way analysis of variance (optional)
	Exercises 9.3
	9.4 Two-way analysis of variance, randomized complete block design
	Exercises 9.4
	9.5 Multiple comparisons
	Exercises 9.5
	9.6 Chapter summary
	9.7 Computer examples
		9.7.1 Examples using R
		9.7.2 Minitab examples
		9.7.3 SPSS examples
		9.7.4 SAS examples
	Exercises 9.7
	Projects for Chapter 9
		9A Transformations
		9B Analysis of variance with missing observations
		9C Analysis of variance in linear models
10. Bayesian estimation and inference
	10.1 Introduction
	10.2 Bayesian point estimation
		10.2.1 Criteria for finding the Bayesian estimate
	Exercises 10.2
	10.3 Bayesian confidence interval or credible interval
	Exercises 10.3
	10.4 Bayesian hypothesis testing
	Exercises 10.4
	10.5 Bayesian decision theory
	Exercises 10.5
	10.6 Empirical Bayes estimates
		10.6.1 Jackknife resampling
		10.6.2 Bootstrap resampling
		10.6.3 Parametric, standard Bayes, empirical Bayes: Bootstrapping and jackknife
	Exercises 10.6
	10.7 Chapter summary
	10.8 Computer examples
		10.8.1 Examples with R
	Project for Chapter 10
		10A Predicting future observations
11. Categorical data analysis and goodness-of-fit tests and applications
	11.1 Introduction
	11.2 Contingency tables and probability calculations
	Exercises 11.2
	11.3 Estimation in categorical data
		11.3.1 Large sample confidence intervals for p
	11.4 Hypothesis testing in categorical data analysis
		11.4.1 The chi-square tests for count data: one-way analysis
		11.4.2 Two-way contingency table: test for independence
	Exercises 11.4
	11.5 Goodness-of-fit tests to identify the probability distribution
		11.5.1 Pearson's chi-square test
		11.5.2 The Kolmogorov-Smirnov test: (one population)
		11.5.3 The Anderson-Darling test
		11.5.4 Shapiro-Wilk normality test
		11.5.5 The P-P plots and Q-Q plots
			11.5.5.1 Steps to construct the P-P plot
	Exercises 11.5
	11.6 Chapter summary
	11.7 Computer examples
		11.7.1 R-commands
		11.7.2 Minitab examples
			11.7.2.1 Chi-square test
	Projects for Chapter 11
		11A Fitting a distribution to data
		11B Simpson's paradox
12 - Nonparametric Statistics
	12.1 Introduction
	12.2 Nonparametric confidence interval
	Exercises 12.2
	12.3 Nonparametric hypothesis tests for one sample
		12.3.1 The sign test
		12.3.2 Wilcoxon signed rank test
		12.3.3 Dependent samples: paired comparison tests
	Exercises 12.3
	12.4 Nonparametric hypothesis tests for two independent samples
		12.4.1 Median test
		12.4.2 The Wilcoxon rank sum test
	Exercises 12.4
	12.5 Nonparametric hypothesis tests for k ≥ 2 samples
		12.5.1 The Kruskal-Wallis test
		12.5.2 The Friedman test
	Exercises 12.5
	12.6 Chapter summary
	12.7 Computer examples
		12.7.1 Examples using R
		12.7.2 Minitab examples
		12.7.3 SPSS examples
		12.7.4 SAS examples
	Projects for Chapter 12
		12A Comparison of Wilcoxon tests with normal approximation
		12B Randomness test (Wald-Wolfowitz test)
	Exercise
13. Empirical methods
	13.1 Introduction
	13.2 The jackknife method
	Exercises 13.2
	13.3 An introduction to bootstrap methods
		13.3.1 Bootstrap confidence intervals
	Exercises 13.3
	13.4 The expectation maximization algorithm
	Exercises 13.4
	13.5 Introduction to Markov chain Monte Carlo
		13.5.1 Metropolis algorithm
		13.5.2 The Metropolis-Hastings algorithm
		13.5.3 Gibbs algorithm
		13.5.4 Markov chain Monte Carlo issues
	Exercises 13.5
	13.6 Chapter summary
	13.7 Computer examples
		13.7.1 Examples using R
		13.7.2 Examples with Minitab
		13.7.3 SAS examples
	Project for Chapter 13
		13A Bootstrap computation
14. Some issues in statistical applications: an overview
	14.1 Introduction
	14.2 Graphical methods
	Exercises 14.2
	14.3 Outliers
	Exercises 14.3
	14.4 Checking the assumptions
		14.4.1 Checking the assumption of normality
		14.4.2 Data transformation
		14.4.3 Test for equality of variances
			14.4.3.1 Testing equality of variances for two normal populations
			14.4.3.2 Test for equality of variances, k≥2 populations
		14.4.4 Test of independence
	Exercises 14.4
	14.5 Modeling issues
		14.5.1 A simple model for univariate data
		14.5.2 Modeling bivariate data
	Exercises 14.5
	14.6 Parametric versus nonparametric analysis
	Exercises 14.6
	14.7 Tying it all together
	Exercises 14.7
	14.8 Some real-world problems: applications
		14.8.1 Global warming
		14.8.2 Hurricane Katrina
		14.8.3 National unemployment
		14.8.4 Brain cancer
		14.8.5 Rainfall data analysis
		14.8.6 Prostate cancer
	14.8 Exercises
	14.9. Conclusion
Appendix I.
Set theory
Appendix II.
Review of Markov chains
Appendix III.
Common probability distributions
Appendix IV.
What is R?
Appendix V.
Probability tables
References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	Z