# MAA - Elementary Statistics

## General Description

• Freshman level statistics course
• Pre-requisite: College Algebra
• Satisfies most general education mathematics requirement
• Satisfies the (basic) statistics requirement for Business Admin, Biology, Psychology, Health Sciences.
• Course incorporates a statistics package (Minitab, SPSS, R, etc)

Possible textbooks include, but are not limited to:

• David S. Moore. The Basic Practice of Statistics, Fifth Edition. New York, NY: W. H. Freeman and Company, 2010.

## Course Objectives

• Data production and analysis
• Probability basics, distributions
• Sampling, estimation with confidence intervals, hypothesis testing, t-test
• Correlation and regression
• Cross-tabulations and chi-square
• Students learn to use a statistical package such as SPSS, R, or Minitab.

## Problem Sets

### Use of Problem Sets

The problem sets were assembled to allow for personalization by individual faculty. The topics covered are fairly standard in a beginning statistics course, but faculty can rearrange the topics and delete any sections they do not wish to cover, or wish to assess by other means. The names of the problem sets are meant to be descriptive and the learning objectives will help you evaluate if the set should be included or not.

A copy of the course can be found at Elementary Statistics at the MAA website

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### Description of Problem Sets

• Set 01 Distributions with Graphs
Students will be able to:
• Use graphs to display data
• Recognize different types of data
• Interpret data from graphs
• Set 02 Distributions with Numbers
Students will be able to:
• Interpret data using numbers
• Compute the mean, and standard deviation
• Identify and use the five number summary.
• Set 03 The Normal Distribution and z-scores
Students will be able to:
• Recognize characteristics of the normal distribution
• Calculate z-scores
• Interpret z-scores
• Set 04 Scatterplots and Correlation
Students will be able to:
• Create scatterplots
• Interpret scatterplots
• Use the concept of correlation to interpret real data
• Identify the shape of the scatterplot by the correlation coefficient.
• Set 05 Regression
Students will be able to:
• Model real life data with a least-squares regression line
• Make predictions using regression
• Set 06 Two-Way Tables
Students will be able to:
• Construct two-way tables
• Calculate relative risks
• Identify causation based on relative risk
• Set 07 Data from Sampling
Students will be able to:
• Distinguish the difference between a population and a sample
• Differentiate between different sampling techniques
• Set 08 Data through Experiments
Students will be able to:
• Distinguish between different experimental designs (double blind, etc)
• Identify components of experiments (control groups, etc)
• Describe the interactions of the components of the experiments
• Identify different types of variables (lurking, explanatory, etc)
• Set 09 Introducing Probability
Students will be able to:
• Define the probability of an event
• Compute conditional probability
• Interpret probabilistic statements
• Set 10 Sampling Distributions
Students will be able to:
• Apply the Central Limit Theorem
• Analyze sampling distributions
• Explain the effect of sample size on sampling distributions
• Comprehend the concept of sampling variation
• Set 11 General Rules of Probability
Students will be able to:
• Calculate probabilities of unions, complements and intersections of events
• Compute conditional probability
• Set 12 Binomial Distributions
Students will be able to:
• Apply the binomial theorem
• Set 13 Inference: Introduction to Confidence Intervals
Students will be able to:
• Calculate and interpret confidence intervals
• Use margin of error to estimate the mean
• Set 14 Inference: Introduction to Hypothesis Testing
Students will be able to:
• Write a null and alternate hypothesis
• Determine the appropriate test based on the alternative hypothesis
• Calculate a test statistic
• Interpret the p-value
• Set 15 Thinking about Inference
Students will be able to:
• Interpret the relationship between sample size and margin of error
• Interpret levels of significance
• Set 16 Inference about a Population Mean
Students will be able to:
• Perform a t-test
• Interpret levels of significance
• Perform a hypothesis test using a critical value
• Set 17 Two-Sample Problems
Students will be able to:
• Write a null and alternate hypothesis for two sample problems
• Perform a two sample means test
• Perform a paired means test
• Distinguish a two sample means test from a paired means
• Interpret levels of significance
• Perform a hypothesis test using a critical value
• Set 18 Inference about a Population Proportion
Students will be able to:
• Perform a hypothesis test on population proportion
• Calculate a confidence interval for a population proportion
• Interpret levels of significance
• Perform a hypothesis test using a critical value
• Set 19 Comparing Two Proportions
Students will be able to:
• Perform a hypothesis test on two proportion
• Calculate a confidence interval for a two proportion
• Interpret levels of significance
• Perform a hypothesis test using a critical value
• Set 20 The Chi-Square Test
Students will be able to:
• Perform a hypothesis test using the chi-square test
• Interpret levels of significance
• Set 21 Inference for Regression
Students will be able to:
• Use a statistical package to find ANOVA
• Interpret ANOVA

WeBWorK Workshop, Raleigh North Carolina March 2013