Statistical Methods

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Statistical Methods Course

Syllabus

Summary

Statistical Methods covers statistical models and methods of analyzing data. These include estimation, tests of significance, analysis of variance, linear regression, and correlation. Students will acquire the necessary statistical basis for using available information to make rational decisions. The prerequisite for MATH 1313 is the algebraic manipulation skill commensurate with that gained in the Preparation Year Program.

Topics Covered:

Will be listed Later

Course Learning Outcomes:

LO1. Identify the different types of data, data sources, and sampling techniques.

LO2. Present data and characterize it.

LO3. Compute probability and identify different probability distributions.

LO4. Estimate parameters and test hypotheses.

LO5. Construct simple linear regression models.

LO6. Conduct quality control and create productivity charts.

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CHAPTERS

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1 Statistics, Data, and Statistical Thinking

PowerPoint | Vocabulary | Notes | Recording: 1 2 3

Lecture 01 – 02

Dates: _____________________

Sec Title of Section

1.1 The Science of Statistics

1.2 Types of Statistical Applications

1.3 Fundamental Elements of Statistics

1.4 Types of Data

1.5 Collecting Data

1.6 The Role of Statistics in Critical Thinking and Ethics

HOMEWORK PROBLEMS: CH 1 in the syllabus

Quiz Test Project: Practical Homework 1 (see recording)

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2 Presenting Data in Tables and Charts

PowerPoint Part1 Part2 | Vocabulary | Notes | recording_4 _5 _6 _7 _9

Lecture: 03-04 - 05

Dates: June 08 - June 09 - June 13 -

Sec: Title of Section:

2.1 Describing Qualitative Data

2.2 Graphical Methods for Describing Quantitative Data

2.3 Summation Notation

2.4 Numerical Measures of Central Tendency

2.5 Numerical Measures of Variability

2.6 Interpreting the Standard Deviation

2.7 Numerical Measures of Relative Standing

2.8 Methods for Detecting Outliers: Box Plots and z-Scores

2.9 Graphing Bivariate Relationships (Optional)

2.10 Distorting the Truth with Descriptive Statistics

HOMEWORK PROBLEMS: CH 2 in the syllabus

Quiz Test Project: Practical Homework 1 (see recording) Due: Saturday, June 13

REVIEW TEST CHAPTER 2 recording_15 recording_16

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3: Probability

PowerPoint | Vocabulary | Notes | recording_ 13 recording_14

Lecture:

Dates:

Title of Section:

Probability
Events, Sample Spaces, and Probability
Unions and Intersections
Complementary Events
The Additive Rule and Mutually Exclusive Events
Conditional Probability
The Multiplicative Rule and Independent Events
Random Sampling
~~Some Additional Counting Rules (Optional)~~
~~Bayes’ Rule (Optional)~~

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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4: Discrete Random Variables

PowerPoint | Vocabulary

Lecture:

Dates:

Title of Section:

4.1 Two Types of Random Variables

4.2 Probability Distributions for Discrete Random Variables

4.3 Expected Values of Discrete Random Variables

4.4 The Binomial Random Variable

~~4.5 The Poisson Random Variable (Optional)~~

~~4.6 The Hypergeometric Random Variable (Optional)~~

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

5: Continuous Random Variables

PowerPoint |

Lecture:

Dates:

Title of Section:

Continuous Random Variables OK
The Probability Distribution for a Discrete Random Variable
The Uniform Distribution
The Normal Distribution
Descriptive Methods for Assessing Normality

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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6: Sampling Distributions

PowerPoint | Notes

Lecture:

Dates:

Title of Section:

Sampling Distributions
The Concept of a Sampling Distribution
Properties of Sampling Distributions: Unbiasedness and Minimum Variance
The Sampling Distribution of x¯ and the Central Limit Theorem

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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7: Inferences Based on a Single Sample Estimation with Confidence Intervals

PowerPoint | Notes

Lecture:

Dates:

Chapter

Sec:

Title of Section:

Inferences Based on a Single Sample: Estimation with Confidence Intervals 298
Identifying and Estimating the Target Parameter 299
Confidence Interval for a Population Mean: Normal ( z ) Statistic 301
Confidence Interval for a Population Mean: Student’s t -Statistic 310
Large-Sample Confidence Interval for a Population Proportion 320
Determining the Sample Size 327
Confidence Interval for a Population Variance (Optional) 334

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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8: Inferences Based on a Single Sample Tests of Hypothesis

PowerPoint | Notes

Lecture:

Dates:

Title of Section:

Inferences Based on a Single Sample: Tests of Hypothesis 349
The Elements of a Test of Hypothesis 350
Formulating Hypotheses and Setting Up the Rejection Region 356
Test of Hypothesis about a Population Mean: Normal (Statistic) 361
Observed Significance Levels: p -Values 367
Test of Hypothesis about a Population Mean: Student’s t -Statistic 373
Large-Sample Test of Hypothesis about a Population Proportion 380
Calculating Type II Error Probabilities: More about b (Optional) 387
Test of Hypothesis about a Population Variance (Optional) 396

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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9: Inferences Based on Two Samples Confidence Intervals and Tests of Hypotheses

PowerPoint | Notes

Lecture:

Dates:

Sec:

Title of Section:

Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses 409
Identifying the Target Parameter 410
Comparing Two Population Means: Independent Sampling 411
Comparing Two Population Means: Paired Difference Experiments 428
Comparing Two Population Proportions: Independent Sampling 440
Determining the Sample Size 447
Comparing Two Population Variances: Independent Sampling (Optional) 450

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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~~10: Analysis of Variance Comparing More than Two Means~~

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11: Simple Linear Regression

PowerPoint | Notes

Lecture:

Dates:

Title of Section:

Simple Linear Regression 549
Probabilistic Models 551
Fitting the Model: The Least Squares Approach 554
Model Assumptions 566
Assessing the Utility of the Model: Making Inferences about the Slope ß1 570
The Coefficients of Correlation and Determination 578
Using the Model for Estimation and Prediction 588
A Complete Example 596

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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12: Multiple Regression and Model Building

PowerPoint | Notes

Lecture:

Dates:

Title of Section:

Multiple Regression and Model Building 612
Multiple-Regression Models 614
PART I: First-Order Models with Quantitative Independent Variables
Estimating and Making Inferences about the ß Parameters 616
Evaluating Overall Model Utility 623 Using the Model for Estimation and Prediction 633

HOMEWORK PROBLEMS:

Quiz Test Project: Due:

Topics:

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~~13: Categorical Data Analysis~~

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~~14: Nonparametric Statistics~~

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