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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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Most popular questions from this chapter

A survey of Chicago. A New York Times/Kaiser foundation survey of Chicagoans showed that they are deeply dissatisfied with the direction of their city, distrust ful of their police force, and divided along racial lines. The poll is based on telephone interviews conducted April 21-May 3, 2016, with 1123 adults who live in Chicago. The samples of telephone exchanges for both landlines and cell phones were randomly selected by a computer from a complete list of exchanges in Chicago (the telephone exchange is the three digits following the area code). Within each exchange, random digits were added to form a complete telephone number, thus permitting access to listed and unlisted numbers alike. Landline respondents are chosen at random within each household on the basis of which member had the most recent birthday. 22 (a) The survey wants the opinion of an individual adult, but a landline phone reaches a household in which several adults may live. In that case, the survey interviewed the adult with the most recent birthday. Why is this preferable to simply interviewing the person who answers the phone? (b) What is the population that this survey wants to describe? Why do you think it is important to include both landline and cellular phones in your sample? (c) Are there residents of Chicago who have telephone numbers that cannot be reached by the survey method described? Explain why this could be a problem. (Hint: How are telephone numbers assigned to cell phone users?)

A Survey of 100,000 Physicians. In 2010 , the Physicians Foundation conducted a survey of physicians' attitude about health care reform, calling the report "a survey of 100,000 physicians." The survey was sent to 100,000 randomly selected physicians practicing in the United States: 40,000 via postoffice mail and 60,000 via email. A total of 2,379 completed surveys were received. 11 (a) State carefully what population is sampled in this survey and what is the sample size. Could you draw conclusions from this study about all physicians practicing in the United States? (b) What is the rate of nonresponse for this survey? How might this affect the credibility of the survey results? (c) Why is it misleading to call the report "a survey of 100,000 physicians"?

Nonresponse. Academic sample surveys, unlike commercial polls, often discuss nonresponse. A survey of drivers began by randomly sampling all listed residential telephone numbers in the United States. Of 45,956 calls to these numbers, 5029 were completed.27 What was the rate of nonresponse for this sample? (Only one call was made to each number. Nonresponse would be lower if more calls were made-)

A sample of households in a community is selected at random from the telephone directory. In this community, \(4 \%\) of households have no telephone, \(10 \%\) have only cell phones, and another \(25 \%\) have unlisted telephone numbers. The sample will certainly suffer from (a) nonresponse. (b) undercoverage. (c) false responses.

The Canadian census. The Canadian government's decision to eliminate the mandatory long-form version of the census and to move these questions to an optional survey has many concerned. Many members of the business community and economists stressed the importance of the census data for crafting public policy. The minister of industry was given the task of defending the government's decision. In response to an argument that making the long form of the census voluntary would skew the data by eliminating the statistical randomness of the survey, the minister replied: "Wrong. Statisticians can ensure validity with a larger sample size." Is the minnister correct? If not, explain in simple terms the error in his statement.

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