Introduction to descriptive and inferential statistics. Topics include collection of data, numerical and graphical descriptive methods, linear correlation and regression, probability concepts and distributions, confidence intervals, and hypothesis testing for means and proportions. Prerequisite: MATH 150 or MATH 170 or MATH 180 or MATH 201. G.E.
Prerequisite(s) / Corequisite(s):
MATH 150 or MATH 170 or MATH 180 or MATH 201.
Course Rotation for Day Program:
Offered Fall and Spring.
Most current editions of the following:
A TI-84 calculator is required for this course. This calculator wil be allowed on most assessment opportunities in this course.
Fundamentals of Statistics
By Sullivan (Prentice Hall) Recommended
Essential Statistics: Exploring the World Through Data
By Gould and Ryan (Pearson) Recommended
To choose appropriate statistical methods to solve real-world problems and understand the limitations of the methods in making predictions and drawing conclusions.
To use appropriate technology to solve statistical problems.
To organize data, communicate the essential features of the data, and interpret data in meaningful ways.
To understand the role of probability in the foundation of modern statistics methods.
Classify data as qualitative or quantitative (discrete or continuous).
Identify advantages and disadvantages of sampling and of common sampling methods.
Distinguish between observational studies and experiments and define different types of experimental design.
Construct frequency distributions for qualitative data and frequency distributions, histograms, stem and leaf plots, and boxplots for quantitative data.
Describe distributions of quantitative data in terms of shape, center, and spread.
Explore the relationship between two qualitative variables using two-way tables.
Explore the relationship between two quantitative variables using scatterplots.
Compute and interpret regression lines and correlation coefficients.
Compute probabilities using the addition rule, the multiplication rule, complements and simple counting techniques.
Determine if events are independent using conditional probabilities.
Construct discrete probability distributions.
Compute and interpret the mean (expected value) and standard deviation of a discrete random variable.
Compute probabilities of binomial experiments.
Compute probabilities and find percentile values of normally distributed data.
Determine if a data set is approximately normally distributed.
Describe and explain the concept of a sampling distribution and the statement of the Central Limit Theorem.
Compute point estimates and interval estimates for a mean or proportion.
Determine the sample size necessary for estimating a mean or proportion to within a given margin of error.
Test hypotheses for a mean or proportion using P-values.
There are many possible topics that could be added to the course but the following are essential:
Introduction to the practice of statistics - Sampling methods - Bias and sampling error - Overview of experimental design - The role of simulation - Qualitative vs. quantitative data - Discrete vs. continuous data
Graphically summarizing data - Frequency distributions - Histograms - Stem and leaf plots - Identifying the shape of a distribution
Numerically summarizing data - Measures of central tendency - Measures of dispersion - The empirical rule - Measures of position - The five-number summary and boxplots
Linear regression and correlation coefficients
Introduction to probability - The vocabulary of probability - Addition rule - Multiplication rule - Complements - Conditional probability and independence - Counting techniques and probability
Discrete probability distributions - Constructing discrete probability distributions - The mean (expected value) of a discrete random variable - The standard deviation of a discrete random variable - Binomial probability distribution
The normal distribution - Essential features of the normal distribution - Applications of the normal distribution - Assessing normality - Sampling distributions and the central limit theorem
Introduction to confidence intervals - Point estimates vs. interval estimates - Margin of error - Confidence intervals for a mean - Confidence intervals for a proportion - Interpreting confidence intervals - Importance of the normally distributed hypothesis - The role of sample size
Introduction to hypothesis testing - The vocabulary of hypothesis testing - The P-value method of hypothesis testing - Testing a hypothesis for a mean
Testing a hypothesis for a proportion
Recommended maximum class size for this course: 30
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical
outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.