Donnell And Maria Are Both Members Of A Population, And A Simple Random Sample Is Being Conducted. If The Chance Of Donnell Being Selected Is 1 290 \frac{1}{290} 290 1 , What Is The Chance Of Maria Being Selected?A. 1 290 \frac{1}{290} 290 1 B.
In statistics, a simple random sample is a subset of individuals selected from a larger population, where every individual has an equal chance of being selected. This method is used to ensure that the sample is representative of the population and to minimize bias. In this article, we will explore the concept of simple random sampling and how it applies to the selection of individuals from a population.
The Concept of Probability
Probability is a measure of the likelihood of an event occurring. In the context of simple random sampling, probability is used to determine the chance of an individual being selected from the population. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Donnell and Maria: A Simple Random Sample
Donnell and Maria are both members of a population, and a simple random sample is being conducted. The chance of Donnell being selected is . We are asked to find the chance of Maria being selected.
The Key to Solving the Problem
The key to solving this problem lies in understanding that the probability of an individual being selected is independent of the probability of another individual being selected. In other words, the selection of one individual does not affect the probability of another individual being selected.
Applying the Concept of Probability
Since the probability of Donnell being selected is , we can assume that the probability of Maria being selected is also . This is because the selection of Donnell does not affect the probability of Maria being selected.
Conclusion
In conclusion, the chance of Maria being selected is also . This is because the probability of an individual being selected is independent of the probability of another individual being selected.
The Importance of Simple Random Sampling
Simple random sampling is an important concept in statistics because it ensures that the sample is representative of the population and minimizes bias. By understanding the basics of simple random sampling, researchers can make informed decisions about their research design and ensure that their results are accurate and reliable.
Real-World Applications
Simple random sampling has many real-world applications, including:
- Market research: Companies use simple random sampling to select a representative sample of customers to conduct market research.
- Medical research: Researchers use simple random sampling to select a representative sample of patients to conduct medical studies.
- Social sciences: Researchers use simple random sampling to select a representative sample of individuals to conduct social science studies.
Common Misconceptions
There are several common misconceptions about simple random sampling, including:
- Misconception 1: The selection of one individual affects the probability of another individual being selected.
- Misconception 2: Simple random sampling is only used in large populations.
- Misconception 3: Simple random sampling is only used in academic research.
Conclusion
In conclusion, simple random sampling is an important concept in statistics that ensures that the sample is representative of the population and minimizes bias. By understanding the basics of simple random sampling, researchers can make informed decisions about their research design and ensure that their results are accurate and reliable.
Frequently Asked Questions
Q: What is simple random sampling? A: Simple random sampling is a method of selecting a subset of individuals from a larger population, where every individual has an equal chance of being selected.
Q: What is the probability of an individual being selected in simple random sampling? A: The probability of an individual being selected is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Q: Does the selection of one individual affect the probability of another individual being selected? A: No, the selection of one individual does not affect the probability of another individual being selected.
Q: What are the real-world applications of simple random sampling? A: Simple random sampling has many real-world applications, including market research, medical research, and social sciences.
Q: What are the common misconceptions about simple random sampling? A: There are several common misconceptions about simple random sampling, including the misconception that the selection of one individual affects the probability of another individual being selected.
References
- Kish, L. (1965). Survey sampling. John Wiley & Sons.
- Cochran, W. G. (1977). Sampling techniques. John Wiley & Sons.
- Snedecor, G. W., & Cochran, W. G. (1989). Statistical methods. Iowa State University Press.
Frequently Asked Questions About Simple Random Sampling =====================================================
In this article, we will answer some of the most frequently asked questions about simple random sampling.
Q: What is simple random sampling?
A: Simple random sampling is a method of selecting a subset of individuals from a larger population, where every individual has an equal chance of being selected.
Q: What is the probability of an individual being selected in simple random sampling?
A: The probability of an individual being selected is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Q: Does the selection of one individual affect the probability of another individual being selected?
A: No, the selection of one individual does not affect the probability of another individual being selected.
Q: What are the advantages of simple random sampling?
A: The advantages of simple random sampling include:
- Representativeness: Simple random sampling ensures that the sample is representative of the population.
- Minimization of bias: Simple random sampling minimizes bias by giving every individual an equal chance of being selected.
- Easy to implement: Simple random sampling is easy to implement, especially in large populations.
Q: What are the disadvantages of simple random sampling?
A: The disadvantages of simple random sampling include:
- Difficulty in large populations: Simple random sampling can be difficult to implement in large populations.
- High cost: Simple random sampling can be expensive, especially in large populations.
- Time-consuming: Simple random sampling can be time-consuming, especially in large populations.
Q: What are the common misconceptions about simple random sampling?
A: There are several common misconceptions about simple random sampling, including:
- Misconception 1: The selection of one individual affects the probability of another individual being selected.
- Misconception 2: Simple random sampling is only used in large populations.
- Misconception 3: Simple random sampling is only used in academic research.
Q: What are the real-world applications of simple random sampling?
A: Simple random sampling has many real-world applications, including:
- Market research: Companies use simple random sampling to select a representative sample of customers to conduct market research.
- Medical research: Researchers use simple random sampling to select a representative sample of patients to conduct medical studies.
- Social sciences: Researchers use simple random sampling to select a representative sample of individuals to conduct social science studies.
Q: How do I implement simple random sampling in my research?
A: To implement simple random sampling in your research, follow these steps:
- Define the population: Define the population you want to study.
- Determine the sample size: Determine the sample size you need to achieve your research goals.
- Use a random number generator: Use a random number generator to select a random sample from the population.
- Ensure representativeness: Ensure that the sample is representative of the population.
Q: What are the limitations of simple random sampling?
A: The limitations of simple random sampling include:
- Difficulty in small populations: Simple random sampling can be difficult to implement in small populations.
- High cost: Simple random sampling can be expensive, especially in small populations.
- Time-consuming: Simple random sampling can be time-consuming, especially in small populations.
Q: Can simple random sampling be used in non-probability sampling?
A: No, simple random sampling cannot be used in non-probability sampling. Simple random sampling is a type of probability sampling, which means that every individual has an equal chance of being selected.
Q: What are the differences between simple random sampling and stratified random sampling?
A: The differences between simple random sampling and stratified random sampling include:
- Sampling method: Simple random sampling uses a random number generator to select a random sample, while stratified random sampling uses a stratification method to select a random sample.
- Representativeness: Simple random sampling ensures that the sample is representative of the population, while stratified random sampling ensures that the sample is representative of the population and the strata.
- Cost: Simple random sampling can be expensive, especially in large populations, while stratified random sampling can be more cost-effective.
Conclusion
In conclusion, simple random sampling is a method of selecting a subset of individuals from a larger population, where every individual has an equal chance of being selected. It has many advantages, including representativeness and minimization of bias, but also has some disadvantages, including difficulty in large populations and high cost. By understanding the basics of simple random sampling, researchers can make informed decisions about their research design and ensure that their results are accurate and reliable.