# Sampling Distributions

• ### Immigration in the U.S.

In this module you will explore some of the impacts of this immigration by examining the characteristics of the foreign-born population, comparing these characteristics to those of the native born population. You will get a chance to explore where immigrants come from, how the composition of the immigrant population has changed, where immigrants settle, and what they do once they get here. Most importantly, you will have the opportunity to test some key hypotheses drawn from the most popular theory used to explain the incorporation of immigrants into the American social and economic mainstream.
• ### High Exposure

This probability activity discusses the differences among various kinds of studies and which types of inferences can legitimately be drawn from each, as well as how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference. The procedure and assessment are provided.
• ### Sampling SIM: Simulation Software

This program allows the student to explore the nature of sampling distributions of sample means and sample proportions. The software provides separate windows for building population distributions, drawing and viewing random samples from the population, exploring the behavior of sampling distributions of sample means, and exploring the behavior of confidence intervals.
• ### A Brief Overview of Switching Theory and Practice

This powerpoint presentation from INFORMS Applied Probability Society provides a brief overview of switches, routers, input-queued crossbars, combined input- and output-queued switches, buffered crossbars, and algorithms for bandwidth partitioning, security, encryption, and deep packet inspection.
• ### **Decision Bonsai

The Decision Bonsai are a hybrid of concept maps and decision trees. They were originally developed to give introductory statistics students a map to inference procedures but have evolved to be used for other topics. The tree is 'grown' during the semester so that students build a picture of the relationships in their mind. Recent work is moving toward the development of more complete concept maps for introductory statistics, statistical quality methods and probability and stochastic processes courses. These Decision Bonsai would be then pointed to at appropriate points in the concept maps.
• ### SurfStat Australia

This website serves as an online textbook for introductory statistics, covering topics such as summarizing and presenting data, producing data, variation and probability, statistical inference, and control charts.
• ### Bootstrapping

This lesson describes bootstrapping in the context of a statistics class for psychology students.
• ### The Probability of Penalizing the Innocent Due to Bad Test Results

This is an example of "growing" a decision tree to analyze two possible outcomes. The tree's branches examine the two possible conditions of employee drug use with corresponding probabilities. This example looks at the final outcome probabilities of being correctly and incorrectly identified versus testing accuracy.
• ### Benford's Law Part 1 - How to Spot Tax Fraud

This page explores Benford's Law: For naturally occurring data, the digits 1 through 9 do not have equal probability of being the first significant digit in a number; the digit 1 has greater odds of being the first significant digit than the others. This law can be used to catch tax fraud because truly random numbers used by embezzlers do not meet this condition.
• ### Star Library: Rectangularity

This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as "stand alone" activities. This allows the educator flexibility in utilizing the activity. Part I illustrates the sampling distribution of the sample mean. Part II illustrates confidence intervals for the population mean. Part III illustrates hypothesis tests for the population mean. This activity is appropriate for use in an introductory college or high school AP statistics course. Key words: sampling distribution of a sample mean, confidence interval for a mean, hypothesis test on a mean, simulation, random rectangles