# MATH 170 Syllabus

### Applied Statistics

Revised: January 2015

## Course Description

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

## Student Learning Goals and Objectives

• Students will be introduced to applications of mathematics in daily experience.
• Student learning will be focused on the development of conceptual understanding rather than computational drill.
• Students will complete a project requiring a mathematical analysis of observations, such that a significant portion of the student project will be statistically based.

## Student Learning Objectives

• Describe the concepts of population and sample, and some of the basic descriptive measures associated with them;
• Explain 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; and
• Interpret estimation and hypothesis testing procedures applied to population means and proportions.

## Text

Roxy Peck, Chris Olsen, and Jay DeVore. Introduction to Statistics and Data Analysis, Fourth Edition. Brooks-Cole/Cengage Learning), 2011.

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: The Role Of Statistics. (1 class days)
Why Study Statistics? The Nature and Role of Variability. Statistics and the Data Analysis Process. Types of Data and Some Simple Graphical Displays.
• Chapter 2: The Data Analysis Process And Collecting Data Sensibly. (2 days)
Statistical studies: Observation and Experimentation. Simple Comparative Experiments. More on Experimental Design. Interpreting and Communicating the Results of Statistical Analyses.
Note: Section 2.5 is optional.
• Chapter 3: Graphical Methods For Describing Data. (2 days)
Displaying Categorical Data: Comparative Bar Charts and Pie Charts. Displaying Numerical Data: Stem-and-Leaf Displays. Displaying Numerical Data: Frequency Distributions and Histograms. Displaying Bivariate Numerical Data. Communicating and Interpreting the Results of Statistical Analyses. Note: Section 3.1 is optional and section 3.4 may be taught concurrenlty with Section 5.1. The topic of density histograms in Section 3.3 is optional
• Chapter 4: Numerical Methods For Describing Data. (4 days)
Describing the Center of a Data Set. Describing Variability in a Data Set. Summarizing a Data Set: Boxplots. Interpreting Center and Variability: Chebyshev's Rule, The Empirical Rule, and z-Scores. Communicating and Interpreting the Results of Statistical Analyses. Note: The topic of trimmed means in Section 4.1 is optional.
• Chapter 5: Summarizing Bivariate Data. (4 days)
Correlation. Linear Regression: Fitting a Line to Bivariate Data. Assessing the Fit of a Line. Communicating and Interpreting the Results of Statistical Analyses.
Note: Sections 5.4 and 5.5 are optional.
• Chapter 6: Probability. (5 days)
Chance Experiments and Events. Definition of Probability. Basic Properties of Probability. Conditional Probability. Independence.
Note: Sections 6.6 and 6.7 are optional.
• Chapter 7: Random Variables and Probability Distributions. (6 days)
Random Variables. Probability Distributions for Discrete Random Variables. Probability Distributions for Continuous Random Variables. Mean and Standard Deviation of a Random Variable. The Binomial Distribution. Normal Distributions.
Note: The topic of Geometric Distributions in Section 7.5, and Sections 7.7 . 7.8 are optional.
• Chapter 8: Sampling Variability And Sampling Distributions. (3 days)
Statistics and Sampling Variability. The Sampling Distribution of a Sample Mean. The Sampling Distribution of a Sample Proportion.
• Chapter 9: Estimation Using A Single Sample. (3 days)
Point Estimation. A Large Sample Confidence Interval for a Population Proportion. A Confidence Interval for a Population Mean. Communicating and Interpreting the Results of Statistical Analyses.
• Chapter 10: Hypothesis Testing Using A Single Sample. (6 days)
Hypotheses and Test Procedures. Errors in Hypothesis Testing. Large-Sample Hypothesis Tests for a Population Proportion. Hypothesis Tests for a Population Mean. Note: Section 10.5 is optional.
• Chapter 11: Comparing Two Populations or Treatments. (3 days)
Inferences Concerning the Difference Between Two Populations or Treatments Means using Independent Samples. Inferences Concerning the Difference Between Two Population or Treatment Means using Paired Samples. Large-scale Inferences Concerning the Difference Between Two Populations or Treatments Proportions. Interpreting the Results of Statistical Analyses.

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