**Complete** the Frankfort-Nachmias and Leon-Guerrero (2018) SPSS® problems and chapter exercises listed below.

- Ch. 6: Chapter Exercises 2, 4, 6, 8, and 12
- Ch. 7: SPSS® Problem 2
- Ch. 7: Chapter Exercises 2, 4, 6, 8, and 12

**Include** your answers in a Microsoft® Word document.

**Click** the Assignment Files tab to upload your assignment.

Please see Chapter 6 material.

- Describe the aims of sampling and basic principles of probability
- Explain the relationship between a sample and a population
- Identify and apply different sampling designs
- Apply the concept of the sampling distribution
- Describe the central limit theorem

Until now, we have ignored the question of who or what should be observed when we collect data or whether the conclusions based on our observations can be generalized to a larger group of observations. In truth, we are rarely able to study or observe everyone or everything we are interested in. Although we have learned about various methods to analyze observations, remember that these observations represent a fraction of all the possible observations we might have chosen. Consider the following research examples.

*Example 1:* The Muslim Student Association on your campus is interested in conducting a study of experiences with campus diversity. The association has enough funds to survey 300 students from the more than 20,000 enrolled students at your school.

*Example 2:* Environmental activists would like to assess recycling practices in 2-year and 4-year colleges and universities. There are more than 4,700 colleges and universities nationwide.1

*Example 3:* The Academic Advising Office is trying to determine how to better address the needs of more than 15,000 commuter students, but determines that it has only enough time and money to survey 500 students.

The primary problem in each situation is that there is too much information and not enough resources to collect and analyze it.

Researchers in the social sciences rarely have enough time or money to collect information about the entire group that interests them. Known as the **population**, this group includes all the cases (individuals, groups, or objects) in which the researcher is interested. For example, in our first illustration, there are more than 20,000 students; the population in the second illustration consists of 4,700 colleges and universities; and in the third illustration, the population is 15,000 commuter students.

**Population** A group that includes all the cases (individuals, objects, or groups) in which the researcher is interested.

Fortunately, we can learn a lot about a population if we carefully select a subset of it. This subset is called a **sample**. Through the process of **sampling**—selecting a subset of observations from the population—we attempt to generalize the characteristics of the larger group (population) based on what we learn from the smaller group (the sample). This is the basis of inferential statistics—making predictions or inferences about a population from observations based on a sample. Thus, it is important how we select our sample.

The term **parameter**, associated with the population, refers to measures used to describe the population we are interested in. For instance, the average commuting time for the 15,000 commuter students on your campus is a population parameter because it refers to a population characteristic. In previous chapters, we have learned the many ways of describing a distribution, such as a proportion, a mean, or a standard deviation. When used to describe the population distribution, these measures are referred to as parameters. Thus, a population mean, a population proportion, and a population standard deviation are all parameters.

We use the term **statistic** when referring to a corresponding characteristic calculated for the sample. For example, the average commuting time for a sample of commuter students is a sample statistic. Similarly, a sample mean, a sample proportion, and a sample standard deviation are all statistics.

**Sample** A subset of cases selected from a population.

**Sampling** The process of identifying and selecting a subset of the population for study.

**Parameter** A measure (e.g., mean, standard deviation) used to describe the population distribution.

**Statistic** A measure (e.g., mean, standard deviation) used to describe the sample distribution.

In this chapter and in the remaining chapters of this text, we discuss some of the principles involved in generalizing results from samples to the population. We will use different notations when referring to sample statistics and population parameters in our discussion. Table 6.1 presents the sample notation and the corresponding population notation.

Table 6.1 Sample and Population Notations

Measure Notation

Sample Notation