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Probability Sampling Quiz 19 (10 MCQs)

This set of multiple-choice questions evaluates understanding of cluster sampling, population division into mutually exclusive subsets, and random selection of clusters. It also covers stratified sampling, dividing populations into strata, and independent sampling from each stratum to ensure representative and unbiased selection. Concepts such as simple random sampling, systematic sampling, and proportional representation are assessed to ensure a comprehensive grasp of probability sampling techniques.

Quiz Instructions

Select an option to see the correct answer instantly.

1. ..... sampling is a probability sample which is distinguished by the following processes: the original population is divided into two or more mutually exclusive and exhaustive subsets (e.g., males and females) and simple random samples of elements from two or more subsets are selected independently of each other

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct, non-overlapping subgroups (strata) based on specific characteristics, and then selecting a simple random sample from each stratum independently.

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

Explanations: Stratified sampling is the correct answer because it involves dividing the population into mutually exclusive and exhaustive subsets (strata) and then selecting simple random samples from each stratum independently. This ensures that each subgroup is adequately represented in the sample.

Option Analysis:

Option A: Systematic sampling involves selecting every kth element from a list after a random start. It does not involve dividing the population into subsets.
Option B: Stratified sampling involves dividing the population into strata and then selecting simple random samples from each stratum independently.
Option C: Single random sampling involves selecting a simple random sample from the entire population without dividing it into subsets.
Option D: Cluster sampling involves dividing the population into clusters and then selecting entire clusters randomly, not individual elements from each cluster.

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

2. In which of the following sampling techniques lottery method can be used?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Simple random sampling is a probability sampling technique where each member of the population has an equal chance of being selected. The lottery method is a common way to achieve this by assigning each member a number and then randomly drawing numbers.

Common Mistakes: A common misunderstanding is that the lottery method can be used in non-probability sampling techniques, such as purposive or quota sampling, where selection is not random.

Explanations: The lottery method is a straightforward way to ensure that each member of the population has an equal chance of being selected, which is a key characteristic of simple random sampling. This method involves assigning a unique number to each member of the population and then using a random process, such as drawing numbers from a hat, to select the sample. This ensures that the sample is representative of the population and unbiased.

Option Analysis:

Option A: Correct. The lottery method is a valid technique for simple random sampling.
Option B: Incorrect. Purposive sampling involves selecting participants based on specific criteria, not random selection.
Option C: Incorrect. Quota sampling involves selecting participants to meet certain quotas, not random selection.
Option D: Incorrect. Snowball sampling involves selecting participants through referrals, not random selection.

3. Which of the following is a technique used to ensure every individual has an equal chance of being selected in a sample?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Systematic sampling is a probability sampling technique where every nth individual from a list is selected after a random start.

Common Mistakes: A common misunderstanding is that convenience sampling, snowball sampling, or judgmental sampling ensures equal chances of selection, which they do not.

Explanations: Systematic sampling ensures that every individual in the population has an equal chance of being selected by using a fixed interval after a random start. This method maintains the principle of equal probability, which is a key characteristic of probability sampling.

Option Analysis:

Option A: Systematic sampling ensures equal probability of selection by using a fixed interval after a random start.
Option B: Convenience sampling relies on easily accessible subjects, not equal probability.
Option C: Snowball sampling relies on referrals from initial subjects, not equal probability.
Option D: Judgmental sampling relies on the researcher's discretion, not equal probability.

4. The Human Resources director decides to take a poll on the current dress code at work. He puts all the employee names in a random generator program, selects 25 names, and emails those 25 employees a survey.

Correct Answer: Correct answer is: (B) Simple random sample.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A simple random sample is a subset of individuals chosen from a larger population in such a way that each individual has an equal chance of being selected.

Common Mistakes: A common misunderstanding is confusing simple random sampling with other sampling methods, such as convenience sampling or systematic sampling. In this case, the use of a random generator program ensures that each employee has an equal chance of being selected, which is a key characteristic of simple random sampling.

Explanations: The Human Resources director uses a random generator program to select 25 names from all employee names. This method ensures that each employee has an equal probability of being chosen, which aligns with the definition of a simple random sample. The use of a random generator program eliminates any bias and ensures that the sample is representative of the entire population.

Option Analysis:

Option A: Systematic sampling involves selecting every kth element from a list after a random start. This is not the case here as the selection is purely random.
Option B: Simple random sampling involves selecting individuals from a population where each individual has an equal chance of being selected. This matches the scenario described.
Option C: Convenience sampling involves selecting individuals based on ease of access, which is not the case here as the selection is random.
Option D: Self-selected (volunteer) sampling involves individuals volunteering to participate, which is not the case here as the employees were selected randomly.

5. If you have a small subgroups of people within the target population and you want a representative sample, which sampling techniques is it best to use?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified sampling is a probability sampling technique that involves dividing the population into distinct subgroups (strata) and then sampling from each subgroup proportionally. This ensures that each subgroup is adequately represented in the sample.

Common Mistakes: A common misunderstanding is that random sampling alone will ensure representation of all subgroups, but this is not always the case, especially if the subgroups are small.

Explanations: Stratified sampling is the best technique when you have small subgroups within the target population and you want a representative sample. By dividing the population into strata and sampling from each stratum, you ensure that each subgroup is adequately represented in the sample. This method is particularly useful when the subgroups have distinct characteristics that are important for the study.

Option Analysis:

Option A: Stratified sampling is the correct choice because it ensures that each subgroup is represented proportionally in the sample.
Option B: Systematic sampling involves selecting every kth element from a list, which may not ensure representation of small subgroups.
Option C: Opportunity sampling is non-probability sampling and relies on convenience, which may not provide a representative sample.
Option D: Random sampling can miss small subgroups if the sample size is not large enough or if the subgroups are not evenly distributed.

6. Ms. Noelle took a proportional number of girls and boys in her class. This type of sampling is called?

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) and then taking a proportional sample from each subgroup. In this case, the population is divided into girls and boys, and a proportional number of each is taken.

Common Mistakes: A common misunderstanding is to confuse stratified sampling with simple random sampling, where every individual has an equal chance of being selected without regard to subgroups.

Explanations: In stratified sampling, the population is divided into distinct subgroups (strata) based on certain characteristics, such as gender. A proportional number of individuals is then sampled from each stratum. Here, Ms. Noelle took a proportional number of girls and boys, which aligns with the definition of stratified sampling.

Option Analysis:

Option A: Correct. Stratified sampling involves dividing the population into subgroups and taking a proportional sample from each subgroup.
Option B: Incorrect. Systematic random sampling involves selecting every kth element from a list after a random start, not dividing into subgroups.
Option C: Incorrect. Simple random sampling involves selecting individuals randomly without regard to subgroups.
Option D: Incorrect. Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters, not proportional sampling from subgroups.

7. To apply the technique of ..... sampling, you first divide the population list into sublists according to some relevant trait and then sample from the sublists.

Correct Answer: Correct answer is: (C) 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 relevant characteristic and then sampling from each subgroup.

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

Explanations: In stratified sampling, the population is first divided into subgroups (strata) based on a relevant trait. This ensures that each subgroup is represented in the sample. Then, samples are taken from each stratum, which allows for a more representative and accurate sample of the entire population.

Option Analysis:

Option A: Simple random sampling does not involve dividing the population into subgroups. Instead, every member of the population has an equal chance of being selected.
Option B: Systematic sampling involves selecting every kth member from a list after a random start, without dividing the population into subgroups.
Option C: Stratified sampling involves dividing the population into subgroups (strata) based on a relevant trait and then sampling from each subgroup.
Option D: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters, rather than dividing into subgroups based on a trait.

Mnemonic: S.T.R.A.T.I.F.I.E.D. - Subgroups, Traits, Represented, Accurate, Traits, Important, Fair, Even, Diverse

8. Which phrase captures the essence of stratified sampling?

Correct Answer: Correct answer is: (C) Subgroups plus random selection.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

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

Common Mistakes: A common misunderstanding is that stratified sampling involves selecting every nth member from a list (systematic sampling) or choosing entire clusters (cluster sampling).

Explanations: Stratified sampling ensures that each subgroup is represented in the sample, which can lead to more accurate and reliable results. The process involves first identifying the subgroups (strata) and then randomly selecting samples from each stratum. This method is particularly useful when the population has distinct subgroups that may differ significantly from each other.

Option Analysis:

Option A: Interval-based fixed selection describes systematic sampling, not stratified sampling.
Option B: Entire clusters chosen randomly describes cluster sampling, not stratified sampling.
Option C: Subgroups plus random selection accurately describes stratified sampling.
Option D: First-come first-served sampling is not a recognized probability sampling method.

9. What kind of sampling technique is the following:Select at random 150 students and send them a survey.

Correct Answer: Correct answer is: (B) Simple random sampling.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Simple random sampling involves selecting a sample from a population in such a way that every member of the population has an equal chance of being included in the sample.

Common Mistakes: A common misunderstanding is confusing simple random sampling with convenience sampling, where the sample is chosen based on ease of access rather than random selection.

Explanations: In the given scenario, selecting 150 students at random and sending them a survey aligns with the definition of simple random sampling. Each student has an equal chance of being selected, and the selection process is unbiased.

Option Analysis:

Option A: Convenience sampling involves selecting individuals who are easiest to reach, which does not apply here as the students are selected randomly.
Option B: Simple random sampling involves selecting individuals randomly, which matches the scenario described.
Option C: Systematic sampling involves selecting every nth individual from a list, which is not the case here as the students are chosen randomly.
Option D: Snowball sampling involves selecting individuals through referrals, which is not applicable here as the students are chosen randomly.

10. A researcher wants to understand more about the coping strategies of nurses working in busy hospitals at night. It is not possible, financially or practically to visit every hospital in country. The researcher decides to choose several specific geographical locations and then obtain list of all hospitals within each location.

Correct Answer: Correct answer is: (D) Cluster sampling.

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Moderate

Concept notes: Cluster sampling involves dividing the population into clusters, which are groups of elements, and then randomly selecting entire clusters to study. This method is often used when it is impractical or too costly to conduct a simple random sample of the entire population.

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

Explanations: The researcher divides the geographical locations into clusters (hospitals within each location) and then selects entire clusters (hospitals) to study. This approach fits the definition of cluster sampling, where the population is divided into clusters and entire clusters are randomly selected for the study.

Option Analysis:

Option A: Simple random sampling involves selecting individuals from the entire population randomly, which is not the case here as the researcher is selecting entire clusters of hospitals.
Option B: Systematic sampling involves selecting every nth individual from a list, which does not apply here as the researcher is selecting entire clusters.
Option C: Stratified sampling involves dividing the population into strata and then sampling from each stratum, which is not the case here as the researcher is selecting entire clusters of hospitals.
Option D: Cluster sampling involves dividing the population into clusters and then selecting entire clusters, which matches the researcher's approach of selecting entire hospitals within specific locations.

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 an unbiased selection.

How does stratified sampling differ from simple random sampling?

Stratified sampling divides the population into subgroups (strata) based on shared characteristics, then randomly selects samples from each stratum, while simple random sampling selects individuals entirely at random without stratification.

What is the purpose of cluster sampling?

Cluster sampling is used to simplify the sampling process by dividing the population into clusters and randomly selecting entire clusters, which can be more practical and cost-effective for large populations.

How can systematic sampling be applied in research?

Systematic sampling involves selecting every nth member from a list after a random start, which can be useful for creating a representative sample when the population is large and ordered in a way that does not introduce bias.

What is the role of the lottery method in probability sampling?

The lottery method is a simple technique used in probability sampling where each member of the population is assigned a number, and numbers are drawn randomly to select the sample, ensuring each member has an equal chance of selection.

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