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91Ó°ÊÓ

Increasing the sample size of an opinion poll will (a) reduce the bias of the poll result. (b) reduce the variability of the poll result. (c) reduce the effect of nonresponse on the poll. (d) reduce the variability of opinions. (e) all of the above.

Short Answer

Expert verified
Increasing sample size reduces the variability of the poll result (option b).

Step by step solution

01

Understanding the problem

We need to determine the effect of increasing the sample size on an opinion poll. Each option describes a potential outcome that might change when the sample size is increased.
02

Examining Bias Reduction

Increasing sample size does not inherently reduce bias because bias is a systematic error related to the survey method or the population being polled. Bias must be addressed through proper sampling techniques and survey design. Thus, option (a) is incorrect.
03

Assessing Variability Reduction

Increasing the sample size typically reduces the variability (margin of error) of the poll results by providing a more accurate estimation of the population parameter. This makes option (b) correct.
04

Evaluating Nonresponse Impact

Nonresponse bias is caused by differences between those who respond to the poll and those who do not. Simply increasing the sample size does not reduce nonresponse bias. Therefore, option (c) is incorrect.
05

Considering Variability of Opinions

The variability of opinions within the population does not change with sample size; sample size only affects the precision of the estimation. Hence, option (d) is incorrect.
06

Evaluating All Options

Since only option (b) is correct, option (e) is not valid as it suggests multiple correct effects.

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Key Concepts

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

Bias Reduction
Understanding bias is crucial in statistics, especially when conducting surveys like opinion polls. Bias refers to systematic errors that skew results in a particular direction. This can occur due to factors such as poor survey design, leading questions, or unrepresentative sample selection.
While increasing the sample size might seem like a solution, it does not directly reduce bias. Larger samples reflect the population more accurately in variability, not in bias.
To specifically reduce bias, survey designers must address the root causes of bias. This involves ensuring a random selection process, neutral question phrasing, and representative sampling strategies. Simply gathering more data won't fix these fundamental design issues. Thus, focus efforts on survey design and methodology to tackle bias.
Variability Reduction
When we talk about variability in the context of surveys, we're referring to the statistical spread of poll results around the true value. It's linked to the concept of margin of error.
Increasing the sample size is an effective way to reduce variability. As more data points are gathered, the poll becomes a more reliable estimate of the population parameter.
  • Larger sample sizes yield more consistent results.
  • The margin of error decreases, making estimates more precise.
This reduction in variability helps in better understanding public opinion by closely approximating true population parameters. Thus, a larger sample enhances the reliability and accuracy of the poll's findings.
Nonresponse Bias
Nonresponse bias arises when the characteristics of those who participate in a survey differ significantly from those who do not. Such discrepancies can lead to skewed results that do not accurately reflect the broader population.
Merely increasing the sample size does not solve the problem of nonresponse bias. Even with a large sample, if a specific subset consistently opts out, the results remain biased.
Combatting nonresponse bias requires strategies like follow-ups or incentives to encourage higher response rates from reluctant participants. It's about ensuring that every segment of the population is adequately represented, which isn't achieved solely through sample size expansion.
Population Parameter Estimation
Estimating population parameters with accuracy is a primary goal in statistical surveys. These parameters, like means and proportions, represent the entire population's characteristics.
A larger sample size enhances the precision of these estimates by reducing the margin of error, leading to results that are close to true population values.
For instance, if estimating an average income level or proportion with a certain opinion, a bigger sample lessens random errors and yields closer approximations.
  • More data points mean more reliability.
  • Results become more robust and trustworthy.
Although increasing sample size is vital, survey methodology must also be precise to avoid errors that even a larger sample cannot fix. Thus, combining adequate sample size with sound survey techniques provides the most accurate population parameter estimates.

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Most popular questions from this chapter

The number of hours alight bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that (a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean \(\mu\) for all bulbs of this type. (b) the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the population distribution. (c) the average burnout time of a large number of bulbs has a distribution with similar shape but not as extreme (skewed, but not as strongly) as the population distribution. (d) the average burnout time of a large number of bulbs has a distribution that is close to Normal. (e) the average burnout time of a large number of bulbs has a distribution that is exactly Normal.

Exercises 69 to 72 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people. Unemployment \((1.1)\) Find the unemployment rate for people with each level of education. How does the unemployment rate change with education?

For Exercises 1 to \(4,\) identify the population, the parameter, the sample, and the statistic in each setting. Unemployment Each month, the Current Population Survey interviews a random sample of individuals in about \(55,000\) U.S. households. One of their goals is to estimate the national unemployment rate. In December \(2009,10.0 \%\) of those interviewed were unemployed.

Multiple choice: Select the best answer for Exercises 43 to \(46,\) which refer to the following setting. The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performance- enhancing drugs are a problem in college sports?" Suppose that 30\(\%\) of all Division I athletes think that these drugs are a problem. Let \(\hat{p}\) be the sample proportion who say that these drugs are a problem. The sampling distribution of \(\hat{p}\) has mean \(\begin{array}{ll}{\text { (a) } 225 .} & {\text { (c) } 0.017 \text { . (e) none of these. }} \\ {\text { (b) } 0.30 .} & {\text { (d) } 0}\end{array}\)

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

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