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Probability Sampling Quiz 14 (10 MCQs)

This set of multiple-choice questions evaluates understanding of stratified sampling, including stratification, random sampling within subgroups, and proportional representation. Concepts covered include population characteristics, subgroup representation, and unbiased selection methods. The questions assess the ability to apply stratified sampling techniques to ensure a representative sample from a heterogeneous population.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Which sampling method uses characteristics to divide groups?

Correct Answer: Correct answer is: (C) Stratified sampling.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified sampling is a probability sampling method where the population is divided into distinct subgroups, or strata, based on specific characteristics. Each stratum is then sampled independently, often using simple random sampling.

Common Mistakes: A common misunderstanding is that stratified sampling is the same as convenience sampling, which involves selecting individuals based on ease of access rather than specific characteristics.

Explanations: Stratified sampling uses characteristics to divide the population into homogeneous subgroups, ensuring that each subgroup is represented in the sample. This method is particularly useful when the population has distinct subgroups that may differ in the variable of interest.

Option Analysis:

Option A: Convenience sampling does not use characteristics to divide groups; it relies on ease of access.
Option B: Simple random sampling does not involve dividing the population into subgroups based on characteristics.
Option C: Stratified sampling involves dividing the population into strata based on specific characteristics, making it the correct answer.
Option D: Snowball sampling is a non-probability sampling method that relies on referrals from initial subjects to recruit additional subjects, not on dividing groups based on characteristics.

2. In this method, the universe is divided into homogeneous groups and sample is taken from each group at random

Correct Answer: Correct answer is: (A) Stratified random sampling.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then taking a random sample from each subgroup.

Common Mistakes: A common misunderstanding is confusing stratified random sampling with cluster sampling, where the population is divided into clusters and entire clusters are randomly selected.

Explanations: In stratified random sampling, the universe is divided into homogeneous groups (strata) based on certain characteristics. A random sample is then taken from each stratum. This ensures that each subgroup is represented in the sample, leading to a more accurate representation of the entire population.

Option Analysis:

Option A: Correct. Stratified random sampling involves dividing the population into homogeneous groups and taking a random sample from each group.
Option B: Incorrect. Unrestricted random sampling does not involve dividing the population into groups; it involves selecting a sample randomly from the entire population without any stratification.
Option C: Incorrect. Systematic sampling involves selecting every nth member of the population after a random start, not dividing the population into groups.
Option D: Incorrect. Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters, not taking samples from each group.

Mnemonic: SRS: Stratify, Randomly Sample

3. Which sampling technique would involve having to form the target population into a randomly ordered list?

Correct Answer: Correct answer is: (E) Systematic sampling.

Exam Relevance: AP Statistics, IB Mathematics, GRE, GMAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a randomly ordered list of the population.

Common Mistakes: A common misunderstanding is that random sampling also requires a list, but it does not necessarily involve a systematic approach.

Explanations: Systematic sampling requires the target population to be arranged in a list. The list is then ordered randomly, and every kth element is selected. This method ensures a structured and systematic approach to sampling, which is why it involves forming a randomly ordered list.

Option Analysis:

Option A: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. It does not require a single randomly ordered list.
Option B: Volunteer sampling involves selecting participants who volunteer, which does not require a list.
Option C: Opportunity sampling involves selecting participants who are conveniently available, which does not require a list.
Option D: Random sampling involves selecting participants randomly, but it does not necessarily require a list.
Option E: Systematic sampling involves selecting every kth element from a randomly ordered list, which matches the requirement of the question.

4. Which of the following is an example of a random sampling technique?

Correct Answer: Correct answer is: (B) Generating a list of numbers by picking numbers out of a hat and matching these numbers to names in your phonebook.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Random sampling is a probability sampling technique where each member of the population has an equal chance of being selected. This ensures that the sample is representative of the population.

Common Mistakes: A common misunderstanding is that any method of selecting a sample is random. However, true random sampling requires each member to have an equal and independent chance of selection.

Explanations: The correct answer is B because it describes a method where each name in the phonebook has an equal chance of being selected. By picking numbers out of a hat and matching them to names, the selection process is unbiased and random.

Option Analysis:

Option A: This method is not random as it includes every person in the phonebook, which is a census, not a sample.
Option B: This method is random as each number has an equal chance of being picked, ensuring each name has an equal chance of being selected.
Option C: This method is not random as it only selects odd-numbered names, which introduces bias.
Option D: This method is not random as it only selects the first 100 names, which introduces bias.

5. The Sullivan County Commissioner of Jurors obtains a list of 42, 763 car owners and constructs a pool of jurors by selecting every 100th name on the list.

Correct Answer: Correct answer is: (E) Systematic sampling.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a list after a random start. In this case, every 100th name is selected from the list of car owners.

Common Mistakes: A common mistake is confusing systematic sampling with simple random sampling. Simple random sampling requires each element to have an equal and independent chance of being selected, whereas systematic sampling follows a fixed interval.

Explanations: The Sullivan County Commissioner of Jurors selects every 100th name from a list of 42,763 car owners. This method of selecting every kth element from a list, after a random start, is characteristic of systematic sampling. The key feature is the fixed interval (every 100th name), which distinguishes it from other sampling methods.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This is not the case here.
Option B: Convenience sampling involves selecting individuals based on ease of access, which is not the method used here.
Option C: Simple random sampling requires each individual to have an equal and independent chance of being selected, which is not the case with a fixed interval.
Option D: Stratified sampling involves dividing the population into strata and then sampling from each stratum. This is not the method used here.
Option E: Systematic sampling involves selecting every kth element from a list after a random start, which matches the method described.

6. The Dean of Mathematics uses a random number generator to generate 100 GHC ID numbers. Each student whose ID is generated will participate in the study.

Correct Answer: Correct answer is: (A) Random sampling.

Exam Relevance: AP Statistics, IB Mathematics, GRE, GMAT

Difficulty: Easy

Concept notes: Random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being selected. This method ensures that the sample is representative of the population.

Common Mistakes: A common misunderstanding is confusing random sampling with other sampling methods like systematic or convenience sampling. In random sampling, each individual is chosen independently and randomly, whereas in systematic sampling, individuals are chosen based on a fixed interval, and in convenience sampling, individuals are chosen based on ease of access.

Explanations: The Dean of Mathematics uses a random number generator to generate 100 GHC ID numbers. Each student whose ID is generated will participate in the study. This method ensures that each student has an equal chance of being selected, which is the defining characteristic of random sampling.

Option Analysis:

Option A: Correct. Random sampling involves selecting individuals randomly, which is what the Dean is doing by using a random number generator.
Option B: Incorrect. Systematic sampling involves selecting individuals based on a fixed interval, not randomly.
Option C: Incorrect. Convenience sampling involves selecting individuals based on ease of access, not randomly.
Option D: Incorrect. Stratified sampling involves dividing the population into subgroups and then randomly selecting from each subgroup, which is not described in the scenario.
Option E: Incorrect. Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters, which is not described in the scenario.

7. As a researcher, you ask the people of your barangay on how they spenttheir money during the community quarantine. You decided to group themaccording to their socio-economic status and then proportionately andrandomly selecting samples from these groups. Which type of sampling areyou using?

Correct Answer: Correct answer is: (C) Stratified.

Exam Relevance: AP Statistics, GRE, GMAT, Research Methods Exams

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) based on certain characteristics, and then randomly selecting samples from each subgroup proportionally.

Common Mistakes: A common mistake is confusing stratified sampling with other types of sampling methods, such as convenience or purposive sampling, which do not involve dividing the population into subgroups.

Explanations: The researcher divided the population into groups based on socio-economic status, which are distinct subgroups (strata). Then, samples were selected randomly and proportionately from each subgroup. This method aligns with the definition of stratified sampling.

Option Analysis:

Option A: Convenience sampling involves selecting individuals who are easiest to reach, which does not involve dividing the population into subgroups.
Option B: Purposive sampling involves selecting individuals based on specific criteria, but it does not necessarily involve dividing the population into subgroups and sampling proportionately.
Option C: Stratified sampling involves dividing the population into subgroups and then randomly selecting samples from each subgroup proportionately, which matches the described method.
Option D: Systematic sampling involves selecting every nth individual from a list, which does not involve dividing the population into subgroups.

Mnemonic: S-S-S: Stratify, Sample, Subgroups

8. Which of the following is not a feature of random sampling?

Correct Answer: Correct answer is: (D) It maximises experiment variances.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Random sampling is a method used to ensure that a sample is representative of the population, which helps in generalizing the results and reducing error. It does not aim to maximize experiment variances.

Common Mistakes: A common misunderstanding is that random sampling increases variability, but in fact, it aims to reduce variability and ensure that the sample is representative of the population.

Explanations: Random sampling is designed to make the sample representative of the population, which helps in generalizing the results and reducing error. It does not aim to maximize experiment variances. Instead, it aims to minimize bias and ensure that the sample accurately reflects the population characteristics.

Option Analysis:

Option A: Random sampling makes the sample representative of the population by ensuring each member of the population has an equal chance of being selected.
Option B: Random sampling ensures generalization of results because the sample is representative of the population, allowing findings to be applied to the broader population.
Option C: Random sampling reduces error and increases precision by minimizing bias and ensuring that the sample accurately reflects the population characteristics.
Option D: Random sampling does not aim to maximize experiment variances; rather, it aims to minimize bias and ensure representativeness.

9. A national hair salon chain is trying to improve their customer service. They divide up their database of customers by hair color and then randomly select 15 clients from each color group to send a questionnaire to.

Correct Answer: Correct answer is: (A) Stratified.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) based on a characteristic, and then randomly selecting samples from each subgroup.

Common Mistakes: A common misunderstanding is confusing stratified sampling with cluster sampling. In cluster sampling, the population is divided into clusters, and entire clusters are randomly selected, whereas in stratified sampling, samples are taken from each stratum.

Explanations: The hair salon chain divides their customers into groups based on hair color, which creates distinct strata. They then randomly select 15 clients from each color group. This method ensures that each subgroup (stratum) is represented in the sample, which is the defining characteristic of stratified sampling.

Option Analysis:

Option A: Correct. The method described matches the definition of stratified sampling.
Option B: Incorrect. Systematic sampling involves selecting every nth member of the population, which is not the case here.
Option C: Incorrect. Cluster sampling involves selecting entire clusters, not individual samples from each cluster.
Option D: Incorrect. The method described is not biased as it uses random selection within each stratum.

Mnemonic: S-S-S: Stratify, Sample, Stratified

10. Which sampling technique will be most appropriate to draw a representative sample of heterogeneous population?

Correct Answer: Correct answer is: (A) Stratified Random.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified random sampling is a probability sampling technique where the population is divided into distinct subgroups (strata) based on specific characteristics, and then random samples are drawn from each stratum. This ensures that each subgroup is represented in the sample, making it particularly effective for heterogeneous populations.

Common Mistakes: A common misunderstanding is that simple random sampling is sufficient for heterogeneous populations. However, simple random sampling may not adequately represent all subgroups within a heterogeneous population.

Explanations: Stratified random sampling is the most appropriate technique for a heterogeneous population because it ensures that each subgroup within the population is adequately represented in the sample. By dividing the population into strata based on relevant characteristics and then randomly selecting samples from each stratum, the method ensures that the sample accurately reflects the diversity of the population.

Option Analysis:

Option A: Stratified Random is the correct choice as it ensures representation from all subgroups within a heterogeneous population.
Option B: Quota sampling is non-probability sampling and does not ensure random selection, which can lead to bias.
Option C: Purposive sampling is non-probability sampling and relies on the researcher's judgment, which can introduce bias.
Option D: Incidental sampling is non-probability sampling and involves selecting individuals who are conveniently available, which can lead to significant bias.

Frequently Asked Questions

What is probability sampling?

Probability sampling is a method of selecting a sample from a population where each member has an equal chance of being chosen, ensuring a representative sample.

How does stratified random sampling work?

Stratified random sampling involves dividing the population into subgroups based on characteristics like socio-economic status, then randomly selecting samples from each subgroup.

Why is random selection important in probability sampling?

Random selection is crucial because it minimizes bias and ensures that the sample accurately reflects the population, reducing sampling error.

What is the purpose of systematic sampling?

Systematic sampling involves selecting every nth item from a randomly ordered list, providing a structured and unbiased selection process.

How does probability sampling help in research?

Probability sampling helps in research by ensuring that the sample is representative of the population, which enhances the validity and reliability of the findings.

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