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MATH 170 Syllabus

Applied Statistics

Revised:  October 2020

Course Description

Descriptive statistics, exploratory data analysis, probability distributions, correlation, regression, estimation, and hypothesis testing. Three semester hours.

Student Learning Objectives

By the end of the course, students should be able to:

  • Describe the concepts of population and sample, and some of the basic descriptive measures associated with them.
  • Explain and utilize graphical methods for data presentation.
  • Connect the concepts of probability, random variables, and distributions.
  • Assess the properties of common distributions, especially the normal and binomial.
  • Synthesize the ideas of correlation and regression.
  • Interpret estimation and hypothesis testing procedures applied to population means and proportions.

 Learning Objectives for Liberal Studies

MATH 170 is a C2 (Mathematics) Liberal Studies Course. Specifically, this course will emphasize the following Liberal Studies learning objective and outcome:

Objective: Problem Solving

 Students will apply appropriate disciplinary methodologies to answer questions and propose solutions to problems within the human and natural worlds.

 As a C2 Course, this course introduces applications of mathematics to daily experience, emphasizing the development of conceptual understanding rather than computational drill. An assignment in which students display an application of mathematics and/or analytical problem solving will be required.

Text

James McClave and Terry Sincich. Statistics, Thirteenth Edition. Pearson, 2017.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

  • Chapter 1: Statistics, Data and Statistical Thinking (0.5 weeks)
    • The Science of Statistics (Optional)
    • Types of Statistical Applications (Optional)
    • Fundamental Elements of Statistics
    • At minimum, cover experimental unit, sample, population and variable
    • Types of Data
    • Collecting Data: Sampling and Related Issues
    • More complex sampling designs on page 13 are optional
    • The Role of Statistics in Critical Thinking and Ethics (Optional) 
  • Chapter 2: Methods for Describing Sets of Data (1 week)
    • Describing Qualitative Data (Optional; students probably know pie chart and bar chart)
    • Graphical Methods for Describing Quantitative Data (Optional; students may know some topics)
    • Numerical Measures of Central Tendency
    • Numerical Measures of Variability
    • Using the Mean and Standard Deviation to Describe Data (Optional)
    • Numerical Measures of Relative Standing
    • Methods for Detecting Outliers: Boxplots and z-Scores
    • Graphing Bivariate Relationships (Optional)
    • Distorting the Truth with Descriptive Statistics (Optional) 
  • Chapter 3: Probability (1.5 weeks)
    • 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
    • Some Additional Counting Rules (Optional)
    • Bayes鈥檚 Rule (Optional) 
  • Chapter 4: Discrete Random Variables (1 week)
    • Two Types of Random Variables
    • Probability Distributions for Discrete Random Variables
    • Expected Values of Discrete Random Variables
    • The Binomial Random Variable
    • The Poisson Random Variable (Optional)
    • The Hypergeometric Random Variable (Optional) 
  • Chapter 5: Continuous Random Variables (0.5 weeks)
    • Continuous Probability Distributions
    • The Uniform Distribution (Optional)
    • The Normal Distribution
    • Descriptive Methods for Assessing Normality (Optional)
    • Approximating a Binomial Distribution with a Normal Distribution (Optional)
    • The Exponential Distribution (Optional) 
  • Chapter 6: Sampling Distributions (1 week)
    • The Concept of a Sampling Distribution
    • Properties of Sampling Distributions: Unbiasedness and Minimum Variance (Optional)
    • The Sampling Distribution of the Sample Mean and the Central Limit Theorem
    • The Sampling Distribution of the Sample Proportion 
  • Chapter 7: Inferences Based on a Single Sample: Estimation with Confidence Intervals (1.5 weeks)
    • Identifying and Estimating the Target Parameter
    • Confidence Interval for a Population Mean: Normal (z) Statistic (Optional)
    • Confidence Interval for a Population Mean: Student鈥檚 t-Statistic
    • Large-Sample Confidence Interval for a Population Proportion
    • Determining the Sample Size
    • Confidence Interval for a Population Variance (Optional) 
  • Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses (2 weeks)
    • The Elements of a Test of Hypothesis
    • Formulating Hypotheses and Setting Up the Rejection Region
    • Observed Significance Levels: p-values
    • Test of Hypothesis about a Population Mean: Normal (z) Statistic (Optional)
    • Test of Hypothesis about a Population Mean: Normal (t) Statistic
    • Large-Sample Test of Hypothesis about a Population Proportion
      • Adjusted CI for a Population Proportion p on page 340 is optional
    • Calculating the Type II Error Probabilities (Optional)
    • Test of Hypothesis about a Population Variance (Optional) 
  • Chapter 9: Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses (1.5 weeks)
    • Identifying the Target Parameter
    • Comparing Two Population Means: Independent Sampling
    • Comparing Two Population Means: Paired Difference Experiments
    • Comparing Two Population Proportions: Independent Sampling
    • Determining the Sample Size (Optional)
    • Comparing Two Population Variances: Independent Sampling (Optional) 
  • Chapter 11: Simple Linear Regression (1.5 weeks)
    • Probabilistic Models
    • Fitting the Model: The Least Squares Approach
    • Model Assumptions (Optional)
    • Assessing the Utility of the Model: Making Inferences about the Slope (Optional)
    • The Coefficients of Correlation and Determination
    • Using the Model for Estimation and Prediction (Optional)
    • A Complete Example (Optional)

 * Note: Most instructors for this course require the use of statistical calculators.