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An opinion poll calls 2000 randomly chosen residential telephone numbers in Portland and asks to speak with an adult member of the household. The interviewer asks, "How many movies have you watched in a movie theater in the past 12 months?" In all, 831 people respond. The sample in this study is (a) all adults living in Portland. (b) the 2000 residential phone numbers called. (c) the 831 people who responded.

Short Answer

Expert verified
The sample is the 831 people who responded.

Step by step solution

01

Understand the Terminology

In this problem, we need to identify the sample used for the study. In statistics, a sample refers to the subset of individuals from a larger population, which is being studied to draw conclusions about the population.
02

Examine the Options

The problem presents three options regarding what constitutes the sample: (a) all adults living in Portland, (b) the 2000 residential phone numbers called, and (c) the 831 people who responded. Our task is to determine which of these options is the actual sample used.
03

Evaluate Each Option

Option (a), all adults living in Portland, represents the entire population, not the sample, because the survey can only reach a subset of individuals. Option (b), the 2000 residential phone numbers called, represents the initial attempt to reach people, but not everyone contacted is part of the sample, as some might not have responded. Option (c), the 831 people who responded, are the individuals from whom data was collected, which defines the actual sample in the context of the study.
04

Determine the Correct Answer

Based on the evaluation, the sample consists of the individuals who actually provided data, making it the 831 people who responded to the survey. This subset is used to draw conclusions about the movie theater attendance of adults in Portland.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sample Definition
In statistics, the concept of a "sample" is fundamental. It refers to a smaller group of individuals selected from a larger population to represent that population in a study. This selection is usually done through random sampling to minimize bias. A sample should accurately reflect the characteristics of the population from which it is drawn.
The aim is to gather insights and draw conclusions about the larger group without having to survey everyone in that group. It's important because tracking every individual in a population can be costly and time-consuming.
When the sample is well-chosen, the results are reliable and can be generalized to the whole population. In our exercise, the sample is the 831 people who responded to the survey. They are the ones providing the data analyzed to understand movie theater attendance in Portland.
Population vs. Sample
Understanding the difference between a population and a sample is crucial in statistics. The population is the entire group you want to draw conclusions about. It includes every individual or instance that could potentially be the subject of the study.
A sample, on the other hand, is a smaller, manageable version of the population. It's selected through various techniques to represent the whole group. The choice of the sample determines how well the results from the study can be generalized to the larger population.
  • Population: A complete group with all possible members. In our exercise, it would be all adults living in Portland.
  • Sample: A subset of the population that participates in the study. For the exercise, this is the 831 people who responded to the survey.
By analyzing the sample, researchers aim to make inferences about the entire population's behavior or characteristics, which is essential for effective decision-making.
Survey Methodology
Survey methodology involves methods and techniques used to gather data from individuals to understand their opinions, behaviors, or characteristics. Its quality largely depends on how well the survey population represents the overall population.
Conducting a survey involves designing questions, selecting the sample, and choosing an appropriate mode of delivery, such as phone calls, online forms, or face-to-face interviews. In this exercise, the survey reached out to 2000 residential phone numbers, demonstrating the random nature of the selection process.
  • Question design: Ask clear and unbiased questions, like "How many movies have you watched in the past 12 months?"
  • Sampling: Ensure the sample accurately represents the population.
  • Data Collection: Gather responses effectively, using methods suitable for reaching the target audience, such as phone calls in this case.
The survey methodology directly affects the reliability and validity of the study. By focusing on key elements of survey methodology, researchers can collect meaningful, actionable data.

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