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91Ó°ÊÓ

Multiple choice: Select the best answer for Exercises 21 to 24. In a poll, I. Some people refused to answer questions. II. People without telephones could not be in the sample. III. Some people never answered the phone in several calls. Which of these sources is included in the \(\pm 2 \%\) margin of error announced for the poll? (a) I only (c) III only (e) None of these (b) II only (d) I, II, and III

Short Answer

Expert verified
(e) None of these

Step by step solution

01

Understand Margin of Error

The margin of error refers to the natural variability that comes from using a sample to estimate information about the whole population. It accounts for random sampling error but not for biases in how data is collected.
02

Identify Each Source of Error

Consider each point in the poll: - **I**: Refusal to answer can lead to nonresponse bias. - **II**: Excluding people without telephones is a coverage bias. - **III**: Not answering calls leads to nonresponse bias as well.
03

Determine What Contributes to Margin of Error

The margin of error accounts for random sampling variability, assuming a properly randomized selection. It does not cover biases such as nonresponse (I, III) or coverage bias (II) which could lead to sampling errors beyond randomness.
04

Match Poll Biases to Margin of Error

The biases mentioned (I, II, III) are forms of systematic error, not random error, and thus are not included in the margin of error. The margin of error is for random sampling error only.

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Key Concepts

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

Nonresponse Bias
Nonresponse bias occurs when individuals selected for a survey do not respond, leading to a significant gap in the data collected. This can skew results because the characteristics of non-respondents may differ from those who do participate. There are several reasons people might not answer, such as refusal to participate, being unreachable, or lack of interest. For instance, in the poll, some individuals might refuse to answer questions or repeatedly not answer their phone calls. Both these situations contribute to nonresponse bias. This type of bias affects the accuracy of survey results because if the non-respondents have different opinions or behaviors than respondents, the findings could be misleading. To mitigate nonresponse bias, researchers can take several approaches:
  • Increase the response rate by sending reminders or follow-up queries.
  • Weight the responses to account for underrepresented demographics.
  • Conduct a nonresponse analysis to determine if those not responding differ significantly from those who do.
Acknowledging and reducing nonresponse bias is crucial for ensuring the credibility and reliability of survey conclusions.
Coverage Bias
Coverage bias arises when the sampling frame – basically the list or method used to identify survey participants – does not accurately represent the entire population. An example from the poll is the exclusion of individuals without telephones, which means those people had zero chance of being selected. This leads to coverage bias because the sample fails to cover segments of the population that might have different opinions or characteristics. Coverage bias can severely limit the generalizability of survey results because it systematically leaves out parts of the population. To address coverage bias, researchers should:
  • Ensure the sampling frame includes all relevant sub-groups within the population.
  • Utilize multiple modes of data collection, such as online, phone, and in-person surveys.
  • Assess the potential scope of coverage bias and adjust the data accordingly.
Understanding coverage bias helps researchers design more inclusive sampling methods, which contribute to more accurate survey findings.
Random Sampling Error
Random sampling error is an inherent part of data collection when using samples to make inferences about a larger population. It represents the variation you expect simply by chance when selecting a random sample. The margin of error, such as the \(\pm 2\%\) mentioned in the poll, quantifies this error. Random sampling error stems from the natural variability between different samples – even if selected randomly – leading to slightly different results each time. Unlike biases, it does not systematically over- or under-represent any part of the population. Instead, it merely reflects the fact that you're making inferences based on a smaller slice of the overall group. To reduce random sampling error:
  • Increase the sample size, as larger samples tend to yield more accurate estimates.
  • Ensure that the sample is as random as possible to minimize sampling variability.
  • Report the margin of error to give a clear picture of the uncertainty in the estimates.
It's essential to distinguish random sampling error from biases since only the former is included in the margin of error calculations.

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