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A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. For each part below, identify the sampling methods described, and describe the statistical pros and cons of the method in the city's context. (a) Randomly sample 200 households from the city. (b) Divide the city into 20 neighborhoods, and sample 10 households from each neighborhood. (c) Divide the city into 20 neighborhoods, randomly sample 3 neighborhoods, and then sample all households from those 3 neighborhoods. (d) Divide the city into 20 neighborhoods, randomly sample 8 neighborhoods, and then randomly sample 50 households from those neighborhoods. (e) Sample the 200 households closest to the city council offices.

Step by step solution

01

Identify (a) as Simple Random Sampling

For part (a), the method used is Simple Random Sampling. This strategy involves selecting 200 households at random from the entire city, without consideration of which neighborhood they belong to. This means that every household has an equal chance of being included in the sample.

02

Evaluate Simple Random Sampling

Pros: Provides a fair representation of the entire city if the sampling is done correctly, assuming there is no systematic bias. Cons: May not capture the unique characteristics or diversity of different neighborhoods.

03

Identify (b) as Stratified Sampling

Part (b) describes Stratified Sampling. The city is divided into 20 neighborhoods (strata), and 10 households are randomly selected from each neighborhood. This ensures all neighborhoods are represented in the sample.

04

Evaluate Stratified Sampling

Pros: Increases representativeness and accuracy by ensuring all parts of the city are included, capturing diversity. Cons: Implementation can be complex and time-consuming as data collectors need access to all neighborhoods equally.

05

Identify (c) as Cluster Sampling

For part (c), Cluster Sampling is used. The city is divided into neighborhoods (clusters), 3 neighborhoods are randomly selected, and all households within those neighborhoods are included in the sample.

06

Evaluate Cluster Sampling

Pros: Cost-effective and practical for large populations. Cons: Results can be biased if selected clusters are not representative of the entire city, as only a few neighborhoods are surveyed.

07

Identify (d) as Multistage Sampling

In part (d), Multistage Sampling is employed. The city is divided into neighborhoods (first stage), 8 neighborhoods are randomly selected (second stage), and then 50 households are randomly sampled from each selected neighborhood (third stage).

08

Evaluate Multistage Sampling

Pros: Provides a balance between cost-efficiency and representativeness. Cons: Complexity in execution and potential biases if selected neighborhoods or households are not representative.

09

Identify (e) as Convenience Sampling

Part (e) uses Convenience Sampling, as it involves selecting 200 households that are closest to the city council offices, without regard for randomness or representation.

10

Evaluate Convenience Sampling

Pros: Easy to implement and low cost. Cons: Highly biased, as it does not represent the city's diversity or spread, leading to potentially unrepresentative and unreliable results.

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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 is a method where each member of a population has an equal chance of being selected for the sample. Imagine pulling names out of a hat; each name has an equal likelihood of being chosen. This method is easy to understand and straightforward to implement when a comprehensive list of the population is available.

In the context of a city survey, choosing 200 households completely at random can provide a fair reflection of the entire city's demographic, assuming there's no bias in the process. However, one downside is that it might not capture specific neighborhood characteristics or represent the diversity within the city. For example, distinct areas with unique socio-economic traits might be underrepresented.

This method ensures fairness, but it also requires a robust process to truly randomize household selection.

Stratified Sampling

Stratified sampling involves dividing a population into distinct subgroups, or strata, and sampling from each group. Think of it as ensuring that every different piece of a puzzle is part of the final picture. In the scenario of a city survey, dividing the city into neighborhoods and choosing households from each ensures that every part of the city is included.

The advantage is that this method increases the accuracy and representativeness of the sample, as every neighborhood, with its unique characteristics, is represented. It can be particularly useful in a diverse setting where certain subgroups might be underrepresented in a random sample.

The challenge, however, is the need for detailed knowledge and access to each neighborhood, complicating the sampling process.

Cluster Sampling

Cluster sampling is a technique where the population is divided into clusters, and a whole cluster or a few clusters are chosen randomly for study. Imagine breaking down the city into neighborhood blocks and choosing a few blocks where every household within those blocks is surveyed.

This approach can be cost-effective and practical, especially when populations are spread out over a large area. It's like focusing your effort on small, manageable sections of the whole population.

The critical downside is that the results may be biased if the selected clusters aren't reflective of the whole population. If the sampled neighborhoods don’t encapsulate the diversity of the entire city, the survey results might not truly reflect city-wide trends.

Multistage Sampling

Multistage sampling combines different sampling methods, much like layering techniques for added detail. First, the city is divided into neighborhoods; then, a sample of these is randomly selected, and finally, households within those chosen neighborhoods are sampled again randomly.

This approach balances representativeness and cost-saving, as it reduces the need to sample the entire city while allowing detailed sampling within specific areas. It offers flexibility by narrowing down from broad geographical areas to individual households.

However, its complexity can lead to potential biases, especially if random selection at any stage is flawed or if the selected neighborhoods differ significantly from others in unmeasured ways.

Convenience Sampling

Convenience sampling involves selecting samples that are easiest to reach. Imagine surveying only the households closest to the city council offices simply because they are nearby. This method is straightforward and low-cost as it requires minimal effort and resources.

However, its major limitation is its high potential for bias. The sample may not be representative of the entire population because it likely misses out on the diversity spread across the city.

For city council surveys, using convenience sampling might result in skewed data, not fully representing the community's needs and characteristics, as it represents only those close to the office location.