© StraighterLine MAT202: Introduction to Statistics

Introduction to Statistics Course Text

This course does not require a text. The primary resources for this course are listed below which are free, online materials.

Rice University: David M. Lane et al.’s Online Statistics Education: An Interactive Multimedia Course of Study

Introductory Statistics Missouri State University: David W. Stockburger’s Introductory Statistics:

Concepts, Models, and Applications Khan Academy’s “Statistics Videos”

Course Description In this course, students will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. Students will learn about how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. After finishing this course, students should be comfortable evaluating an author’s use of data and be able to extract information from articles and display that information effectively. Students will also be able to understand the basics of how to draw statistical conclusions. This course will begin with descriptive statistics and the foundation of statistics, move onto probability and random distributions, the latter of which enables statisticians to work with several aspects of random events and their applications. Finally, students will examine a number of ways to investigate the relationships between various characteristics of data.

Course Objectives Upon successful completion of this course, you will be able to:

define the meaning of descriptive statistics and statistical inference, describe the importance of statistics, and interpret examples of statistics in a professional context;

distinguish between a population and a sample; explain the purpose of measures of location, variability, and skewness; apply simple principles of probability; compute probabilities related to both discrete and continuous random variables; identify and analyze sampling distributions for statistical inferences; identify and analyze confidence intervals for means and proportions; compare and analyze data sets using descriptive statistics, parameter estimation,

hypothesis testing; explain how the central limit theorem applies in inference;

© StraighterLine MAT202: Introduction to Statistics

calculate and interpret confidence intervals for one population average and one population proportion;

differentiate between type I and type II errors; conduct and interpret hypothesis tests; identify and evaluate relationships between two variables using simple linear

regression; and use regression equations to make predictions.

Course Prerequisites

Successful completion of College Algebra is recommended before taking Introduction to Statistics.

Important Terms

In this course, different terms are used to designate tasks: Practice Exercise: A non­graded set of problems that where skills discussed in a

topic are practiced. Graded Quiz: A graded online assessment that is usually shorter than a graded

exam. Graded Exam: A graded online assessment that is comprehensive.

Course Evaluation Criteria

StraighterLine provides a percentage score and letter grade for each course. See Academic Questions section in FAQ for further details on percentage scores and grading scale. A passing percentage is 70% or higher.

If you have chosen a Partner College to award credit for this course, your final grade will be based upon that college's grading scale. Only passing scores will be considered by Partner Colleges for an award of credit. There are a total of 1000 points in the course:

Unit Assessment Points Available

1 Graded Quiz 1 500 across all Graded Quizzes (total)

© StraighterLine MAT202: Introduction to Statistics

2 Graded Quiz 2

4 Graded Quiz 3

5 Graded Quiz 4

6 Graded Quiz 5

7 Final Graded Exam 500

Total 1000

Course Units and Objectives Unit Unit Title Subunit Title Objectives

1 Statistics and Data

The Science of Statistics and Its Importance

Methods for Describing Data

Apply various types of sampling methods to data collection;

Create and interpret frequency tables;

display data graphically and interpret the following types of graphs: stem plots, histograms, and boxplots;

identify, describe, and calculate the following measures of the location of data: quartiles and percentiles;

identify, describe, and calculate the measures of the

© StraighterLine MAT202: Introduction to Statistics

center of mean, median, and mode; and

Identify, describe, and calculate the following measures of the spread of data: variance, standard deviation, and range.

2 Elements of Probability and Random Variables

Classical Probability Model

Random Variables

Understand and use the terminology of probability;

Determine whether two events are mutually exclusive and whether two events are independent;

Calculate probabilities using the addition Rules and multiplication rules;

Construct and interpret Venn diagrams;

Apply useful counting rules in the context of combinational probability;

Identify and use common discrete probability distribution functions;

Calculate and interpret expected values;

Identify the binomial probability distribution, and apply it appropriately;

Identify the Poisson probability distribution, and apply it appropriately.

3 Normal Distributions and Sampling Distributions

Normal Distributions

The Concept of Sampling Distributions

Sampling Distributions for Common Statistics

Identify and use continuous probability density functions;

Identify the normal probability distribution, and apply it appropriately;

Apply the central theorem to approximate sampling distributions;

Describe the role of sampling distributions in inferential statistics;

Interpret and create graphs of a probability distribution for the mean and a discrete variable;

© StraighterLine MAT202: Introduction to Statistics

Describe a sampling distribution in terms of repeated sampling;

Compute the mean and standard deviation of the sampling distribution of the population;

Identify or approximate a sampling distribution based on the properties of the population;

Compare and evaluate the sampling distributions of different sample sizes; and

Compare and evaluate the performance of different estimators based on their sampling distributions.

4 Estimation with Confidence Intervals

Point Estimators and Their Characteristics

Confidence Intervals

Explain the central limit theorem, and use it to construct confidence intervals;

Compare t­distribution and normal distribution;

Apply and interpret the central limit theorem for sample averages;

Calculate and interpret confidence intervals for population averages and one population proportions;

Calculate and interpret confidence intervals for the difference of two population proportions and means; and

Interpret the student­t probability distribution as the sample size changes.

5 Hypothesis Test

Elements of Hypothesis Testing

Tests of Population Means

Comparing the Proportions of Two Populations

Differentiate between type I and type II errors;

Describe hypothesis testing in general and in practice;

Interpret and explain how to conduct hypothesis tests for a single population mean and population proportion, when the population standard deviation is unknown;

© StraighterLine MAT202: Introduction to Statistics

Chi­Square Applications

Classify hypothesis tests by type.

Interpret and explain how to conduct hypothesis tests about two proportions and means;

Interpret and explain how to conduct chi­square significance testing

6 Linear Regression

The Regression Model

Fitting the Model

Discuss basic ideas of linear regression and correlation;

Identify the assumptions that inferential statistics in regression are based on;

Compute the standard error of a slope;

Test a slope for significance; Construct a confidence

interval on a slope; and Calculate and interpret the

correlation coefficient.

7 Review Review Review and Final Exam