# Investigating the Social World

# ASA TRAILS

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**Technique 10: Sampling Distribution (Binomial)**

Teaching Objectives/Student Learning Outcomes: To provide a concrete example of a sampling distribution; to demonstrate the statistical properties of such a distribution, specifically, that its mean is equal to the underlying population parameter and that 95% of the sample results lie within plus or minus two standard deviations of that value; to provide experience with multistage, systematic sampling and the use of a random numbers table; and to discuss sampling frame bias. As a result, students should be able to describe the concept of sampling distribution, including some of its statistical properties, use a random numbers table, draw a simple multistage systematic sample, and discuss bias in sampling frames.

In this exercise, we will investigate the concept of statistical sampling by following the basic debate that arose over how to conduct the 2000 census. You will learn the difference between a sample and a population. You will learn the real-life implications of sampling strategies, both in terms of the type of data that is collected and the policy implications that result from the use of the census data. This exercise is used as the first step in a series of three exercises on this topic, one for each level of difficulty.

**Constructing a National Sample of Cities (Intermediate Level)**

The purpose of this exercise is to learn how to construct a national sample for a hypothetical survey. Many survey projects fail to generate significant or believable findings because the researcher did not pay careful attention to sampling procedures. If the sample of people interviewed inadequately represents the target population for the research, the findings will not be generalizable, that is they can’t be said to apply to the larger group.