MATH 2261, Principles of Statistics, Assignments

Each assignment is based on a course objective, and is designed to illustrate that objective. The purpose of the assignments is to build an understanding of statistical principles and processes.

The following assignments can be completed with any principles of statistics text book, and many can be completed using only the online class resource links .

Assignment 1: Recognize and Interpret Data Sets - Using Appropriate Tools
The Tools of Statistics: What Are Statistics and How Do We Use Them?

Please answer the following questions:
1.) What is the purpose of a graphical presentation of data?

2.) Qualitative data is by definition data that is in discrete categories or classes. Given a particular data set, discuss circumstances in which you could group such data into fewer or more categories or classes, and why it would be appropriate. (Format: Assume a data set--a sports team, for example--then discuss the possible classifications of that data set and justifications for each one.)

3.) Discuss the advantages and disadvantages of mean, median, and midrange as measures of central location.

4.) Discuss the advantages and disadvantages of percentiles and z-scores as measures of relative position.

Assignment 2 - Concepts and Calculations of Probabilities
Expectations and Events: The Nature of Probability

Please complete the following questions and exercises:

1.) Discuss probability as a concept, and "statistical probability" as an application.

2.) Exercise: The statistical probability of a given outcome in a coin flip is 50% (50% heads, 50% tails). Flip a coin 100 times, track the results, and discuss. Do you notice any patterns within the results? How would you expect your results to differ if you did the exercise again?

3.) Discuss gambling as a probabilistic exercise. What is the nature of probability in gambling games? Why is it said that "the house always has an edge?

4.) The Weather is considered a "chaotic system" because it is nearly impossible to predict the weather in even the smallest physical space. Comment, using statistics and probability, on how meteorolgists "predict" the weather.

Assignment 3 - Probability Distributions and Key Components

Please answer the following questions:
1.) Discuss probability distribution.

2.) Describe an experiment (in the sense of the word "experiment" which we us in statistics) which you do on a regular basis.

3.) Give a pair of events which should be independent, and discuss why they should be independent (you may need to identify the population in which the events occur).

Assignment 4 - Methods of Sampling and Resulting Data Types
Margin of Error: Statistics and the Polling Process

Please complete the following exercises:

1.) Discuss the difference between "sampling" and "census."

2.) Discuss opinion polling as a sampling exercise.

3.) Discuss the extent to which any opinion poll is a binomial experiment.

Assignment 5 - Confidence Interval and Sample Size

1.) Discuss confidence intervals

2.) How do statisticians determine the proper sample size for a given study?

3.) What are the consequences of choosing an inappropriate sample size?

Assignment 6 - Hypothesis Testing Procedures

Please answer the following questions:

1.) Discuss hypothesis testing.

2.) Discuss the relationship between tests of hypothesis and confidence intervals

3.) Discuss the central limit theorem as it applies to binomial experiments

4.) Discuss the notion of causality in relation to correleation.

5.) Discuss some variables which you would expect to be negatively correlated.

Final Paper Assignment - Lies, D*#$@*# Lies, and Statistics
The Use of Statistics to Mislead

Statistics are merely ways of interpreting reality. They can be used to confirm or dispute most any assertion about events or people.

Develop a paper providing examples of times that statistics have been used to make a case or persuade, when such persuasion was not exactly true. Present your examples as a series of case studies, including the event or issue involved, the statistics used, and the underlying misuse of statistics to mislead.