# Statistics Introduction

**Author(s):**
Mezbahur
Rahman
,
Han
Wu
,
Deepak
Sanjel

**Edition:
**
1

**Copyright:
**
2012

**Pages:
**
214

**Edition:
**
1

**Copyright:
**
2012

**Pages:
**
214

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This textbook is meant to introduce statistics to the general audience. It is also meant for the first college course in statistics irrespective of the student’s area of study. The audience is assumed to have no higher mathematics background than college algebra. The authors avoided broad explanations using varieties of examples to keep the length of the textbook short. Only the materials that can be covered in a semester and that are vital in introducing the concepts of statistics are included. Partial questions that have little value in the real world are mostly avoided. Complete questions are given to emphasize the concepts. More emphasis is given for the word problems.

The emphasis of this textbook is on concepts of statistics, and hence repetitive numerical and graphical descriptive methods are avoided. When the audience has the knowledge of key vocabularies in statistics and familiarity with the statistical concepts, they will be able to implement other methods without much difficulty.

*Preface
Acknowledgments*

**Chapter 1: Introduction**

1.1 Introduction

1.2 Population Parameters and Sample Statistics

1.3 Historical Background

1.4 Types of Data

1.5 Need of a Sample

1.6 Data Collection Methods

1.7 Sampling Methods

1.8 Technology in Statistical Analysis

*Exercises*

**Chapter 2: Descriptive Statistics**

2.1 Organizing and Displaying Data

2.2 Frequency Table

2.3 Graphical Displays

2.4 Numerical Measures

2.5 Measures of Central Tendency

2.6 Measures of Variation

2.7 Measures of Position

*Exercises*

**Chapter 3: Inferential Statistics**

3.1 Definitions

3.2 Basic Approaches to Computing Probability

3.3 Relationships among Events

3.4 Conditional Probability

3.5 Counting

*Exercises*

**Chapter 4: Discrete Probability Distributions**

4.1 Definitions

4.2 Discrete Probability Distributions

4.3 Other Situations

4.4 Mean or Expected Value of a Discrete Random Variable

4.5 Variance and Standard Deviation of a Discrete Random Variable

*Exercises*

**Chapter 5: Continuous Probability Distributions**

5.1 Definitions

5.2 The Normal Distribution

5.3 Sampling Distributions

5.4 The Central Limit Theorem

5.5 Normal Approximation to the Binomial Distribution

*Exercises*

**Chapter 6: Inferences about Population Parameters**

6.1 Inferences about Population Proportion *p*

6.2 Inferences about Population Mean μ

6.3 Inferences about Population Variance σ2

6.4 Testing Statistical Hypotheses Regarding Population Mean μ

6.5 Testing Statistical Hypotheses Regarding Population Proportion *p*

6.6 Testing Statistical Hypotheses Regarding Population Variance σ2

*Exercises*

**Chapter 7: Comparing Two Population Parameters**

7.1 Comparing Two Population Proportions

7.2 Comparing Two Independent Population Means

7.3 Comparing Two Dependent or Matched Population Means

7.4 Comparing Two Independent Population Variances

*Exercises*

**Chapter 8: Chi-square Tests and Analysis of Variance**

8.1 Chi-square Goodness-of-fit Test

8.2 Test for Homogeneity

8.3 Test for Homogeneity

8.4 Analysis of Variance

*Exercises*

**Chapter 9: Association between Two Variables**

9.1 Correlation Coefficient

9.2 Simple Linear Regression

*Exercises*

**Appendix I**

I.1 Solutions for Selected Exercises from Chapter 1

I.2 Solutions for Selected Exercises from Chapter 2

I.3 Solutions for Selected Exercises from Chapter 3

I.4 Solutions for Selected Exercises from Chapter 4

I.5 Solutions for Selected Exercises from Chapter 5

I.6 Solutions for Selected Exercises from Chapter 6

I.7 Solutions for Selected Exercises from Chapter 7

I.8 Solutions for Selected Exercises from Chapter 8

I.9 Solutions for Selected Exercises from Chapter 9

**Appendix II**

* Table 1:* Random Number Generating Table

* Table 2: *Standard Normal Cumulative Probability

*Table 3:* t-Distribution Percentiles

*Table 4:* Chi-square Distribution Percentiles

* Table 5:* F-distribution Percentiles

*Index*

**Mezbahur Rahman**

**Han Wu**

**Deepak Sanjel**

This textbook is meant to introduce statistics to the general audience. It is also meant for the first college course in statistics irrespective of the student’s area of study. The audience is assumed to have no higher mathematics background than college algebra. The authors avoided broad explanations using varieties of examples to keep the length of the textbook short. Only the materials that can be covered in a semester and that are vital in introducing the concepts of statistics are included. Partial questions that have little value in the real world are mostly avoided. Complete questions are given to emphasize the concepts. More emphasis is given for the word problems.

The emphasis of this textbook is on concepts of statistics, and hence repetitive numerical and graphical descriptive methods are avoided. When the audience has the knowledge of key vocabularies in statistics and familiarity with the statistical concepts, they will be able to implement other methods without much difficulty.

*Preface
Acknowledgments*

**Chapter 1: Introduction**

1.1 Introduction

1.2 Population Parameters and Sample Statistics

1.3 Historical Background

1.4 Types of Data

1.5 Need of a Sample

1.6 Data Collection Methods

1.7 Sampling Methods

1.8 Technology in Statistical Analysis

*Exercises*

**Chapter 2: Descriptive Statistics**

2.1 Organizing and Displaying Data

2.2 Frequency Table

2.3 Graphical Displays

2.4 Numerical Measures

2.5 Measures of Central Tendency

2.6 Measures of Variation

2.7 Measures of Position

*Exercises*

**Chapter 3: Inferential Statistics**

3.1 Definitions

3.2 Basic Approaches to Computing Probability

3.3 Relationships among Events

3.4 Conditional Probability

3.5 Counting

*Exercises*

**Chapter 4: Discrete Probability Distributions**

4.1 Definitions

4.2 Discrete Probability Distributions

4.3 Other Situations

4.4 Mean or Expected Value of a Discrete Random Variable

4.5 Variance and Standard Deviation of a Discrete Random Variable

*Exercises*

**Chapter 5: Continuous Probability Distributions**

5.1 Definitions

5.2 The Normal Distribution

5.3 Sampling Distributions

5.4 The Central Limit Theorem

5.5 Normal Approximation to the Binomial Distribution

*Exercises*

**Chapter 6: Inferences about Population Parameters**

6.1 Inferences about Population Proportion *p*

6.2 Inferences about Population Mean μ

6.3 Inferences about Population Variance σ2

6.4 Testing Statistical Hypotheses Regarding Population Mean μ

6.5 Testing Statistical Hypotheses Regarding Population Proportion *p*

6.6 Testing Statistical Hypotheses Regarding Population Variance σ2

*Exercises*

**Chapter 7: Comparing Two Population Parameters**

7.1 Comparing Two Population Proportions

7.2 Comparing Two Independent Population Means

7.3 Comparing Two Dependent or Matched Population Means

7.4 Comparing Two Independent Population Variances

*Exercises*

**Chapter 8: Chi-square Tests and Analysis of Variance**

8.1 Chi-square Goodness-of-fit Test

8.2 Test for Homogeneity

8.3 Test for Homogeneity

8.4 Analysis of Variance

*Exercises*

**Chapter 9: Association between Two Variables**

9.1 Correlation Coefficient

9.2 Simple Linear Regression

*Exercises*

**Appendix I**

I.1 Solutions for Selected Exercises from Chapter 1

I.2 Solutions for Selected Exercises from Chapter 2

I.3 Solutions for Selected Exercises from Chapter 3

I.4 Solutions for Selected Exercises from Chapter 4

I.5 Solutions for Selected Exercises from Chapter 5

I.6 Solutions for Selected Exercises from Chapter 6

I.7 Solutions for Selected Exercises from Chapter 7

I.8 Solutions for Selected Exercises from Chapter 8

I.9 Solutions for Selected Exercises from Chapter 9

**Appendix II**

* Table 1:* Random Number Generating Table

* Table 2: *Standard Normal Cumulative Probability

*Table 3:* t-Distribution Percentiles

*Table 4:* Chi-square Distribution Percentiles

* Table 5:* F-distribution Percentiles

*Index*

**Mezbahur Rahman**

**Han Wu**

**Deepak Sanjel**