/*! 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 49 The Canadian census. The Canadia... [FREE SOLUTION] | 91Ó°ÊÓ

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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.

Short Answer

Expert verified
The minister is incorrect; larger sample size cannot fix self-selection bias in a voluntary survey.

Step by step solution

01

Understanding the Issue

The issue is whether making a census voluntary and increasing its sample size can ensure the validity and representativeness of the data collected. The concern is that by making it voluntary, the randomness of the sample might be compromised.
02

Identifying Key Concepts

Understand the role of randomness in statistical sampling. A random sample ensures that every individual in the population has an equal chance of being selected, providing a representative snapshot of the whole population.
03

Analyzing Voluntary Sampling

In a voluntary survey, the decision to participate is made by the respondents, which can lead to a self-selection bias. This means that certain groups of people might be more likely to respond than others, skewing the results.
04

Evaluating the Minister's Statement

The minister's statement suggests that increasing the sample size can counteract the lack of randomness. However, a larger sample size does not correct for self-selection bias. If the sample is not random, increasing size alone will not make it more representative.
05

Concluding on the Statement's Validity

Increasing the sample size does not ensure the validity of voluntary data collection if the sample is not random. The lack of randomness creates bias that cannot be corrected just by having more participants.

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Key Concepts

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

Random Sample
A random sample is a cornerstone of statistical accuracy when conducting surveys or censuses. It ensures every individual in a population has an equal chance of being chosen. This produces results that are representative of the entire population, reflecting its diversity without bias.

To achieve a random sample, researchers often use methods like drawing names from a hat or employing computer algorithms that select participants randomly. This process eliminates the influence of human choice and personal biases, making the findings more credible and generalizable to the whole population. When a sample lacks randomness, the results may fail to accurately depict the population’s true tendencies and characteristics.
Self-Selection Bias
Self-selection bias occurs when individuals get to choose whether or not to participate in a survey or study. This voluntary choice can lead to skewed data because the respondents might not represent the broader group you’re studying.

For example, in a voluntary survey, people who are enthusiastic about the topic might participate more than those who are indifferent. This means findings might over-represent extreme opinions and under-represent moderate ones.
  • Individuals who have strong feelings about the topic may participate more.
  • Those who lack interest or knowledge might not participate at all.
This type of bias is problematic because it makes it difficult to obtain an honest snapshot of the population’s actual views or characteristics. Counteracting self-selection requires strategies that compel or encourage a random distribution of participation.
Sample Size
Sample size refers to the number of observations or participants selected from a population for a study. While a larger sample size can increase the precision of the estimate, it does not inherently correct for sample bias.

A common misconception is that simply increasing the sample size will solve issues related to bias in data. While having more participants can reduce the margin of error and provide more robust results, it cannot fix inherent biases in how the sample was selected.

When randomness is absent from sampling, no amount of participants can accurately represent the entire population. Thus, combining large sample sizes with a random selection process is essential to generating valid and reliable data.
Voluntary Survey
Voluntary surveys rely on participants' willingness to respond, making them prone to certain biases that can compromise the quality of the data collected.

These surveys often attract respondents with specific interests or strong opinions about the topic. For instance, if a survey about community services is voluntary, those who are actively engaged or dissatisfied might be more likely to respond compared to those who are content or indifferent.
  • Participation depends on personal choice.
  • Results can skew towards opinions of those who feel strongly.
This self-selection process means voluntary surveys often lack the randomness required for statistical accuracy. The results can give a distorted view of the population's actual perceptions, leading to misinformed policy-making or business decisions.

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Most popular questions from this chapter

NPR Facebook Survey. In 2010, National Public Radio (NPR) conducted a survey of preferences and habits of its Facebook fans by recruiting respondents through messages posted on its Facebook page. The survey was conducted online and deployed July \(12-19\). A total of 40,043 respondents began the survey, with 33,304 completing all questions. It was found that people accessed NPR on the radio, at the website NPR_org, through iPhone apps, and several other platforms. Asked about time spent with NPR, about \(20 \%\) of respondents indicated that they spent more than three hours per day, including radio listening. (a) Here is what NPR says about the survey methodology: "Respondents were self-selected and the resulting sample is non-random-therefore a margin of error cannot be calculated, and the survey results cannot be projected to any population other than the sample itself."18 Why can't inference about any population be made? (b) Suppose that people who spent more time with NPR were more likely to respond to the survey. Do you think the true percentage of NPR's Facebook fans who spend more than three hours with NPR is higher or lower than the \(20 \%\) found from the survey? Explain why.

How Accurate Is the Poll? A Pew Research Center survey on Teens, Social Media \& Technology at the beginning of 2015 included 1060 teens, of which 614 were white, non-Hispanic; 101 were black, non-Hispanic; 236 were Hispanic; and 109 were other races or ethnic groups. Each teen sampled was asked about technology usage, including access to mobile devices, social media usage, and video game playing. The margin of error (we will give more detail in later chapters) was reported as \(63.7 \%\) for the entire sample. When considering technology usage of only the Hispanic teens, the margin of error was reported as \(68.1 \% .4\) What do you think explains the fact that estimates for Hispanic teens were less precise than for the entire sample?

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?)

Sampling on Campus. You would like to start a club for psychology majors on campus, and you are interested in finding out what proportion of psychology majors would join. The dues would be \(\$ 35\) and used to pay for speakers to come to campus. You ask five psychology majors from your senior psychology honors seminar whether they would be interested in joining this club and find that four of the five students questioned are interested. Is this sampling method biased, and if so, what is the likely direction of bias?

Online news polls. On January 30, 2015, the Los Angeles Times ran an online poll on its website and asked readers the question, If the NFL comes to Las Angeles, which team would be the best fit? The St. Louis Rams, San Diego Chargers and Oakland Raiders are all an year-to-year leases, unhappy with their current venues, and mulling a possible relocution to L.A. Readers clicked on one of three buttons to vote: a picture of the Oakland Raiders logo, a picture of the San Diego Chargers logo, and a picture of the St. Louis Rams logo. In all, 12,212 (33\%) selected the Oakland Raiders, 2038 (6\%) selected the San Diego Chargers, and 22,721 (61\%) selected the St. Louis Rams. 25 (a) What is the sample size for this poll? (b) The sample size for this poll is much larger than is typical for polls such as the Gallup Poll. Explain why the poll may give unreliable information, even with such a large sample size.

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