/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 A Twitter Poll. In September 201... [FREE SOLUTION] | 91Ó°ÊÓ

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A Twitter Poll. In September 2019, ProgressPolls asked the question "Do you think the Democrats have a valid reason for wanting to impeach Trump?" Of the 1437 votes cast, \(91 \%\) said no. This poll was a Twitter poll. A CNN random digit dialing telephone poll of 1003 respondents in September 2019 asked the question "In your view, why do most Democrats in Congress support impeachment of Donald Trump?" Thirty eight percent responded "Because they are out to get Donald Trump at all costs." Explain to someone who knows no statistics why the two polls can give such widely differing results and which poll is likely to be more reliable.

Short Answer

Expert verified
The CNN poll is more reliable due to its random sampling method, which better represents the overall population compared to Twitter's self-selected participants.

Step by step solution

01

Understand Sampling Method

The Twitter Poll conducted by ProgressPolls is a type of voluntary response sampling where participants choose whether to participate. This can result in a sample that is not representative of the wider population, as it may attract individuals with strong opinions on the subject.
02

Analyze Respondent Demographics

On Twitter, users are self-selected and may have a specific demographic, interest, or bias not reflective of the general population. Twitter users might be younger and more technologically savvy, with particular interest groups more likely to engage.
03

Assess CNN Poll Methodology

The CNN poll used random digit dialing, which is a method of collecting a random sample of the population. This technique is designed to reach a broad demographic spectrum, including people who are not specifically active on social media like Twitter.
04

Consider Reliability and Generalization

Random sampling (as done by CNN) is generally more reliable than voluntary response (as done by Twitter) because it reduces bias by giving all members of the population a chance to be selected. Therefore, results from the CNN poll are more likely to reflect the views of the general population.
05

Conclusion on Poll Reliability

The CNN random digit dialing poll is likely to be more reliable because it uses a systematic sampling method that better represents the overall population, whereas the Twitter poll might reflect a more biased group of opinions.

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Key Concepts

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

Voluntary Response Sampling
Voluntary response sampling is a technique where participants decide for themselves if they want to join the survey. This method is often used in places like online polls where anyone can choose to take part. However, one major disadvantage is that it's quite prone to bias. Typically, people who feel strongly about an issue are more likely to participate. This means that the sample could be skewed towards people with similar, often extreme, opinions. For example, in a Twitter poll asking about political views, individuals with intense opinions are more likely to respond, which might not accurately represent the average view of the population. Voluntary response sampling is convenient, but care should be taken when interpreting the results. It's important to recognize that this type of sampling does not usually reflect a wide, unbiased segment of the population.
Random Sampling
Random sampling is a powerful method used to select a group of respondents that truly reflect the larger population. This method ensures that every individual has an equal chance of being selected to participate. For instance, the CNN poll used random digit dialing to get a sample, aiming to reach people from diverse backgrounds and different walks of life, rather than a specific interest group, like Twitter users.
  • With random sampling, you reduce the risk of bias significantly because it captures a wide spectrum of the population.
  • You can trust the results more since it mirrors the diversity of views and opinions across the population.
  • This method focuses on fairness and representativeness, ensuring the gathered data is as objective as possible.
By using this systematic approach, surveys like the CNN poll offer a more reliable picture of the public opinion, which makes them a stronger tool for generalization to real-world contexts.
Bias in Surveys
Bias in surveys can seriously affect the reliability of the results. It occurs when certain groups are over- or under-represented. There are a few common reasons surveys might be biased. For instance, voluntary response surveys often have bias because they attract those with strong opinions. Meanwhile, random sampling aims to minimize bias by giving every potential participant an equal chance of being asked.
There are several types of biases that can affect surveys:
  • Selection Bias: When the sample is not randomly chosen, certain populations may be overrepresented or underrepresented. This can lead to results that don't accurately reflect the broader audience.
  • Response Bias: When participants answer in a way they think is expected, or when the survey's wording itself leads respondents to a particular answer.
  • Non-response Bias: Occurs when a significant portion of selected respondents do not participate in the survey, which may skew the results.
Understanding bias is crucial because it helps identify which survey results can be trusted. Reducing bias leads to more accurate, valid conclusions that better represent the full spectrum of public opinion.

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Most popular questions from this chapter

Ring-no-answer. A common form of nonresponse in telephone surveys is "ring-no- answer." That is, a call is made to an active number, but no one answers. The Italian National Stat istical Institute looked at nonresponse to a government survey of households in Italy during the periods January 1 to Easter and July 1 to August 31 . All calls were made between 7 and 10 P. M., but \(21.4 \%\) gave "ring-no-answer" in one period versus \(41.5 \%\) "ring-no-answer" in the other period. 30 Which period do you think had the higher rate of no answers? Why? Explain why a high rate of nonresponse makes sample results less reliable.

Canadian Health Care Survey. The Thirteenth Annual Health Care in Canada Survey, conducted by POLLARA Research in May and June 2018, is a survey of the opinions of the Canadian public and health care providers on a variety of health care issues, including quality of health care, access to health care, health and the environment, and so forth. According to POLLARA, the survey was based on telephone interviews and included nationally representative samples of 1,500 members of the Canadian public, 100 doctors, 100 nurses, 100 pharmacists and 100 health managers. Public results are considered to be accurate within \(\pm 2.5 \%\), while the margin of error for results for doctors, nurses, pharmacists and managers is \(\pm 9.8 \% .33\) a. Why is the accuracy greater for the public than for health care providers and managers? b. Why do you think the researchers sampled the public as well as health care providers and managers?

A Survey of 100,000 Physicians. In 2010, the Physicians Foundation conducted a survey of physicians' attitudes about health care reform, saying that the report was "a survey of 100,000 physicians." The survey was sent to 100,000 randomly selected physicians practicing in the United States: 40,000 via postal 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"?

Off-Campus Housing. A university's housing and residence office wants to know how much students pay per month for rent in off-campus housing. The university does not have enough on-campus housing for students, and this information will be used in a brochure about student housing. The housing office obtains a list of the 12,304 students who live in off-campus housing and have not yet graduated and mails a questionnaire to a randomly selected group of 200 of these students. Only 78 questionaires are returned. a. What is the population in this study? Be careful: about what group does the office want information? b. What is the sample? Be careful: from what group does the office actually obtain information? The important message in this problem is that the sample can redefine the population about which information is obtained.

Cluster Sampling. Cluster sampling begins by dividing the population into separate groups, or clusters. An SRS of the clusters is selected, and individuals in the cluster are sampled. If all the individuals in a cluster are sampled, this is called one-stage cluster sampling. If a random sample of individuals in a cluster is sampled, this is called two-stage sampling. Cluster sampling can be convenient when the individuals in a cluster are easily sampled as a group, such as all people in a neighborhood for a door-to- door survey. Here is a simple example of one-stage cluster sampling. All students at a small college are required to live in dormitories. There are 25 such dormitories on campus, each with 30 students. a. To select a cluster sample of 150 students, do the following. Label the dormitories from 01 to 25. Choose an SRS of 5 dormitories from the list of the 25. If you use Table \(\mathrm{B}\), enter the table at line 121 and indicate which dormitories you selected. Your cluster sample is the 150 students in these dormitories. b. How many dormitories would you have to sample if you wanted a sample of 100 students?

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