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In Problems 11-22, identify the type of sampling used. Suppose a political strategist wants to get a sense of how American adults aged 18 years or older feel about health care and health incurance (a) In a political poll, what would be a good frame to use for obtaining a sample? (b) Explain why simple random sampling may not guarantee that the sample has an accurate representation of registered Democrats, registered Republicans, and registered Independents. (c) How can stratified sampling guarantee this representation?

Short Answer

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(a) A good frame could be voter registration records or a national registry. (b) Simple random sampling might not ensure accurate political representation due to chance variations. (c) Stratified sampling divides the population into subgroups to ensure proportional representation of each political group.

Step by step solution

01

- Understand the Polling Frame

A frame is a list or other device used to define a researcher's population of interest. For a political poll about health care and health insurance among American adults aged 18 years or older, the frame could include voter registration records, licensed drivers, or a national registry of residents. This ensures that the sample is drawn from a comprehensive list of the target population.
02

- Random Sampling Limitations

Simple random sampling (SRS) gives each member of the population an equal chance of being selected. However, SRS may not capture the political diversity (registered Democrats, Republicans, and Independents) accurately because it relies purely on chance. Large variations in the subgroups could occur, resulting in a misrepresentation.
03

- Stratified Sampling Advantage

Stratified sampling divides the population into subgroups (strata) based on a characteristic, such as political affiliation. By ensuring each stratum is represented proportionally in the sample, stratified sampling achieves a more accurate representation of each subgroup. For instance, if 35% of the population are registered Democrats, 35% of the sample will be taken from the Democrats' stratum, and similarly for Republicans and Independents.

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Key Concepts

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

simple random sampling
Simple random sampling (SRS) is a fundamental method used in statistics for selecting a sample from a larger population. In SRS, every member of the population has an equal chance of being included in the sample. Imagine putting all members' names into a hat and drawing names without looking.
This method is straightforward and helps to eliminate bias in selecting a sample.
But it's not always perfect. For example, when polling about political affiliations, SRS might not capture the diversity accurately.
Random chance could lead to more of one group (like Democrats) being chosen over others (like Republicans or Independents). This could result in an unbalanced sample that does not represent the true population.
Therefore, while SRS is useful for simplicity, it may not always provide a sample truly reflective of the population's composition.
stratified sampling
Stratified sampling is a more refined approach compared to simple random sampling. Here, the population is divided into distinct subgroups or 'strata' that share a similar characteristic, such as political affiliation.
Each subgroup is then sampled in proportion to its size within the population. This ensures representation across all key segments.
For instance, if you know that 30% of the population are Democrats, 40% are Republicans, and 30% are Independents, you divide the population into these three subgroups.
Next, you conduct random sampling within each subgroup. This way, 30% of your total sample will be Democrats, 40% will be Republicans, and 30% will be Independents.
This method guarantees that every subgroup is appropriately represented in the final sample, leading to a more accurate and reliable understanding of the entire population's opinions.
polling frame
A polling frame is a crucial component in the sampling process. It refers to the list or database from which a sample is drawn.
For a political survey, the frame should be a comprehensive list of American adults aged 18 years or older. Examples of such frames could include voter registration records, driver license databases, or national registries.
The key is to use a frame that is as inclusive as possible to avoid leaving out any segments of the population.
A well-constructed polling frame ensures that every potential respondent within the defined population has a chance of being selected for the sample.
Without a proper frame, some groups might be overrepresented or underrepresented, leading to biased results and incorrect conclusions.
Therefore, the choice of a polling frame can significantly influence the accuracy and reliability of the survey outcomes.

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Most popular questions from this chapter

Discuss how a randomized block design is similar to a stratified random sample. What is the purpose of blocking?

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A researcher has recruited 20 volunteers to participate in a study. The researcher wishes to measure the effect of alcohol on an individual's reaction time. The 20 volunteers are randomly divided into two groups. Group 1 serves as a control group in which participants drink four 1-ounce cups of a liquid that looks, smells, and tastes like alcohol in 15 -minute increments. Group 2 serves as an experimental group in which participants drink four 1 -ounce cups of 80 -proof alcohol in 15 -minute increments. After drinking the last 1 -ounce cup, the participants sit for 20 minutes. After the 20 -minute resting period, the reaction time to a stimulus is measured. (a) What type of experimental design is this? (b) Use Table I in Appendix A or a random-number generator to divide the 20 volunteers into groups 1 and 2 by assigning the volunteers a number between 1 and \(20 .\) Then randomly select 10 numbers between 1 and \(20 .\) The individuals corresponding to these numbers will go into group \(1 .\)

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