McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
1. Designing a Study
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Exercise 1 Page 727

What are the differences between a survey, an observational study, and an experiment? A population consists of all the members of a group of interest. A sample is a subset of the population.

Type of Study: Survey
Sample: The students in the study
Population: The student body

Practice makes perfect

We are told that the randomly selected group of students is asked to fill the following form.

Our goal is to determine whether the given situation describes a survey, an experiment, or an observational study, then identify the sample and suggest a population from which it may have been selected. Let's do these things one at a time.

Type of Study

We want to determine the type of study being conducted in the described situation.

A group of high school students is randomly selected and asked to complete the form shown.

To do so, let's first recall the different types of studies and their definitions.

Study Type Definition
Survey Data are collected from responses given a sample regarding their characteristics, behaviors, or opinions.
Observational Study Members of a sample are measured or observed without being affected by the study.
Experiment The sample is divided into two groups — an experimental group that undergoes a change and a control group that does not undergo a change. The effect on the experimental group is then compared to the control group.

In our situation, the data are obtained from opinions given by people who return the form. Therefore, the situation describes a survey.

Sample and Population

A population consists of all the members of a group of interest. Since it may be impractical to examine every member of a population, a sample — a subset of the population — is sometimes selected to represent the population. The sample can then be analyzed to draw conclusions about the entire population.

Let's consider our situation.

A group of high school students is randomly selected and asked to complete the form shown.

Here, the population consists of the student body. The sample consists of the students who were randomly selected and participated in the study.