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Chapter 1: Problem 17

Explain the following four sampling techniques. a. Simple random sampling b. Systematic random sampling c. Stratified random sampling d. Cluster sampling

Short Answer

Expert verified
Simple random sampling gives equal chance for every item in the population to get selected. Systematic random sampling selects every kth item. Stratified random sampling divides population into groups and then does random sampling within each group. Cluster sampling divides population into clusters, selects some clusters randomly, and includes all items from chosen clusters.

Step by step solution

01

Explanation of Simple Random Sampling

Simple random sampling is a type of probability sampling method in which all members of the population have an equal chance of being selected. This type of sampling is easy to implement and the results can be generalized to the whole population.
02

Explanation of Systematic Random Sampling

Systematic random sampling is a type of probability sampling method where elements of the population are arranged in some order. The starting point is selected randomly and then every kth element in the list is selected. This type of sampling is easy to use and helps to ensure an unbiased representation of the population.
03

Explanation of Stratified Random Sampling

Stratified random sampling is a type of probability sampling method which divides the total population into smaller groups or strata based on shared characteristics. Then, a simple random sampling is carried out within each stratum. This method ensures that specific sub-categories of the population are adequately represented within the sample.
04

Explanation of Cluster Sampling

Cluster sampling is a probability sampling method where the entire population is divided into groups or clusters, usually geographically. A random sample of these clusters is chosen, then all members of selected clusters are included in the study. This method can be cost-effective and practical when the population is widely spread or difficult to access.

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Key Concepts

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

Understanding Simple Random Sampling
Simple random sampling is often considered the purest form of probability sampling. Imagine you have a jar filled with hundreds of colored balls, each representing a different person in a population. If you were to blindfold yourself and pick a ball, each ball has the exact same chance of being chosen.
This is the essence of simple random sampling, where every member of the population stands an equal chance of selection.

Some key advantages include:
  • It is straightforward and easy to understand and implement.
  • The results of sampling can be effectively generalized to the greater population.
However, despite its simplicity, it might require a complete list of the population, which is sometimes hard to obtain. Additionally, simple random sampling may not be the most efficient method if the population is widespread.
Exploring Systematic Random Sampling
Systematic random sampling streamlines the random selection process by adding an element of order. First, you arrange your list in a particular sequence. Let's assume you have a list of names or numbers.
Then, you randomly select a starting point in the list and proceed to pick every kth item from there.

This method boasts distinct advantages such as:
  • Simplicity and ease of use in selecting candidates.
  • Ensures even dispersion across a list, potentially minimizing bias.
Nonetheless, systematic random sampling might introduce a hidden bias if there is an underlying pattern in the list that correlates with the population traits being important for the study.
Navigating Stratified Random Sampling
Stratified random sampling takes a more nuanced approach by dividing the entire population into distinct subgroups or "strata" based on specific, shared characteristics. For example, a researcher studying healthcare access might divide the population by age or income levels.
Once these strata are established, a simple random sample is drawn from each one.

The benefits of this method include:
  • Ensuring each subgroup is properly represented in the sample.
  • Increasing the precision of overall data estimates by reducing variability within strata.
However, it requires detailed awareness of the population to correctly form those strata and is generally more complex and time-consuming to organize compared to other sampling methods.
Understanding Cluster Sampling
Cluster sampling is a practical and efficient method, especially when dealing with large and geographically dispersed populations. The population is divided into clusters, usually on a geographical basis or another natural division.
Then, rather than sampling individuals, entire clusters are chosen randomly, and all members within these clusters are included in the analysis.

Cluster sampling is particularly beneficial because:
  • It reduces travel and administrative costs when dealing with a widespread population.
  • Allows for the study of populations that are clustered in small regions.
On the downside, it may introduce a higher level of sampling error if the chosen clusters do not suitably represent the diversity of the overall population.

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Most popular questions from this chapter

In which sampling technique do all samples of the same size selected from a population have the same chance of being selected?

A federal govemment think tank wanted to investigate whether a job training program helps the families who are on welfare to get off the welfare program. The researchers at this agency selected 10,000 families at random from the list of all families that were on welfare. Of these 10,000 families, the agency randomly selected 5000 families and offered them free job training. The remaining 5000 families were not offered such job training. After 3 years the two groups were compared in regard to the percentage of families who got off welfare. Is this an observational study or a designed experiment? Explain.

Indicate whether each of the following constitutes data collected from a population or a sample. a. A group of 25 patients selected to test a new drug b. Total items produced on a machine for each year from 2001 to 2015 c. Yearly expenditures on clothes for 50 persons d. Number of houses sold by each of the 10 employees of a real estate agency during 2015

Eight randomly selected customers at a local grocery store spent the following amounts on groceries in a single visit: \(\$ 216, \$ 184\). \(\$ 35, \$ 92, \$ 144, \$ 175, \$ 11\), and \(\$ 57\), respectively. Let \(y\) denote the amount spent by a customer on groceries in a single visit. Find: a. \(\Sigma y\) b. \((\Sigma y)^{2}\) c. \(\Sigma y^{2}\)

Explain the difference between an observational study and an experiment.
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