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Suppose that you were asked to help design a survey of adult city residents in order to estimate the proportion that would support a sales tax increase. The plan is to use a stratified random sample, and three stratification schemes have been proposed. Scheme 1: Stratify adult residents into four strata based on the first letter of their last name \((\mathrm{A}-\mathrm{G},\) \(\mathrm{H}-\mathrm{N}, \mathrm{O}-\mathrm{T}, \mathrm{U}-\mathrm{Z})\) Scheme 2: Stratify adult residents into three strata: college students, nonstudents who work full time, nonstudents who do not work full time. Scheme 3: Stratify adult residents into five strata by randomly assigning residents into one of the five strata. Which of the three stratification schemes would be best in this situation? Explain.

Short Answer

Expert verified
Scheme 2 seems to be the best choice for the survey design in this scenario, as occupation and educational status are factors likely to influence opinions on a sales tax increase. This scheme will provide a stratified random sample representative of these different groups in the city.

Step by step solution

01

Analyze Scheme 1

The first stratification scheme is: dividing people based on the first letter of their last name. While this scheme randomly divides the population, it does not seem to really reflect any meaningful characteristic related to opinions on a sales tax increase. Remember, a sales tax might affect different demographic groups differently.
02

Analyze Scheme 2

This scheme categorizes individuals based on their employment status or student status. This seems more relevant to the issue at hand, as occupational status and income level could influence opinions on sales tax increase. The economic impact of such increases might be felt differently by different groups, students, working full time employees, and those not working full time.
03

Analyze Scheme 3

In the third scheme, residents are randomly assigned into one of five strata. Assigning residents randomly in this manner creates no guarantee of heterogeneity across strata. There will be no way to ensure that the strata are truly representative of different demographic groups in the city.
04

Determine the Best Scheme

Based on the above analysis, Scheme 2 seems to be the most fitting, as it stratifies residents in a way meaningful to the survey topic. It will likely provide the most representative sample in terms of opinions on sales tax increase.

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Key Concepts

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

Survey Design
Survey design is a crucial part of any research or study that aims to obtain reliable data. When designing a survey, it's essential to tailor it to get accurate and relevant feedback from participants. The choice of survey questions, the format, and the sampling method can significantly affect the results. For instance, including targeted questions that consider the participants' backgrounds can lead to more insightful data.
One of the main objectives of survey design is to minimize biases and maximize the reliability of the responses. This can be achieved through meticulous questionnaire crafting and thoughtful consideration of how the survey is administered. An effectively designed survey helps to ensure that the findings are both valid and applicable to the broader population.
  • Clearly define the survey's purpose.
  • Identify the target population.
  • Develop questions that are direct and unbiased.
  • Select an appropriate sampling method for representative data.
Demographic Analysis
Demographic analysis is a process of gathering and examining data about the characteristics of a specific population. This analysis often includes variables such as age, gender, occupation, and education level. By understanding these characteristics, researchers can gain insights into how various groups might respond differently to certain questions or topics, such as a sales tax increase.
In the context of the given exercise, conducting demographic analysis helps in selecting a stratification scheme that reflects the population accurately. It's crucial to account for the diversity within a population to ensure that the survey captures the varying perspectives of different demographic groups. This, in turn, leads to more generalizable and meaningful results.
  • Analyze age, gender, income levels, and occupational data.
  • Identify differences in opinions across demographic groups.
  • Predict potential impacts of policy changes on specific groups.
Sampling Techniques
Sampling techniques are methods used to select individuals from a population to participate in a survey or study. These techniques play a vital role in ensuring that the sample is representative of the larger population. Stratified sampling, in particular, involves dividing the population into subgroups, or strata, based on shared characteristics, which can increase the precision of survey estimates.
In stratified sampling, careful attention must be given to how strata are defined. For example, the exercise discusses three different stratification schemes, only one of which considers the social and economic characteristics likely to influence opinions. An effective sampling technique increases the likelihood that survey results accurately reflect the population's views.
  • Determine the aim of the survey and define relevant strata.
  • Ensure each stratum is appropriately sized to reflect population distribution.
  • Use stratified sampling to reduce variance and improve representativeness.

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