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91Ó°ÊÓ

When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.

Short Answer

Expert verified
Fewer clusters with more individuals are better for heterogeneous clusters because they capture the overall population's diversity.

Step by step solution

01

Understanding Cluster Sampling

Cluster sampling is a technique used in statistics where the population is divided into separate groups, called clusters. A random sample of these clusters is then selected for analysis.
02

Defining Heterogeneous Clusters

Heterogeneous clusters are groups where individuals within the clusters are diverse or different from each other. This means each cluster is a microcosm of the population.
03

Advantages of Fewer Clusters

Having fewer clusters with more individuals is advisable for heterogeneous clusters because it ensures that each cluster captures the diversity of the population. It reduces the risk of data loss due to variability within clusters.
04

Reducing Sampling Error

With fewer clusters, the sampling error is minimized because the samples taken from these clusters are more likely to be representative of the entire population’s diversity.
05

Conclusion

In conclusion, using fewer clusters with more individuals in cluster sampling is better for heterogeneous clusters to ensure that each sample accurately reflects the diversity of the entire population.

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Key Concepts

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

heterogeneous clusters
Cluster sampling is an excellent method for collecting data. It works best when used with heterogeneous clusters. In these clusters, individuals are very different from each other, reflecting the entire population's diversity.
Each cluster is like a small-scale version of the whole population. This variety within clusters makes our samples more reliable.
When we have fewer clusters but with more individuals in each, we capture a wider array of characteristics. This approach helps ensure our data is truly representative. Imagine taking a handful of colorful candies from various jars. If we take fewer handfuls but from fuller jars, we get better chances of getting all sorts of candies and colors.
This technique allows us to gather detailed insights about population traits without having to survey everyone individually.
sampling error
Sampling error is the difference between the sample results and the true population results.
In cluster sampling, we can minimize sampling errors by choosing fewer but larger clusters. When clusters are filled with diverse individuals, our sample mimics the population better.
Consider measuring how tall different tree types grow in a forest. If we group mixed species together and measure fewer, larger groups, it gives a better approximation of the forest's overall height.
By capturing a broad range of characteristics within fewer clusters, the sampling error reduces. This makes our results more accurate and reliable.
Reducing sampling error means having more confidence that our sample accurately reflects the population.
statistical diversity
Statistical diversity is crucial for good research practice. It ensures that our samples include all the variations present in the population. This makes our findings more valid and generalizable.
If each cluster mirrors the entire population's variety, the sample taken from these clusters will be statistically diverse.
Think of a patchwork quilt made from different fabrics. Each fabric piece is different but, when combined, they represent the whole quilt well. Similarly, few but large heterogeneous clusters capture diverse traits effectively.
This diversity within clusters reflects the overall population, providing a rich source of data. Higher statistical diversity reduces the chance of missing out on important population details, making our study more comprehensive.

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Most popular questions from this chapter

Suppose a fundraiser holds a raffle for which each person who enters the room receives a ticket numbered 1 to \(N,\) where \(N\) is the number of people at the fundraiser. The first person to arrive receives ticket number 1 , the second person receives ticket number \(2,\) and so on. Determine the level of measurement for each of the following interpretations of the variable ticket number. (a) The winning ticket number. (b) The winning ticket number was announced as \(329 .\) An attendee noted his ticket number was 294 and stated, "I guess I arrived too early." (c) The winning ticket number was announced as \(329 .\) An attendee looked around the room and commented, "It doesn't look like there are 329 people in attendance."

Why is a high response rate desired? How would a low response rate affect survey results?

In Problems 11-22, identify the type of sampling used. A pharmaceutical company wants to conduct a survey of 30 individuals who have high cholesterol. The company has obtained a list from doctors throughout the country of 6600 individuals who are known to have high cholesterol. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

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?

In Problems 11-22, identify the type of sampling used. A farmer divides his orchard into 50 subsections, randomly selects \(4,\) and samples all the trees within the 4 subsections to approximate the yield of his orchard.

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