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Sampling Quiz 42 (10 MCQs)

This set of multiple-choice questions evaluates understanding of sampling methods, including accessible population, class list, cluster sampling, and disproportionate stratified sampling. It tests the ability to identify samples, distinguish between population and sample, and understand concepts like random selection, cluster identification, and survey methodology. The questions cover population inference, research generalization, and the representativeness of samples.

Quiz Instructions

Select an option to see the correct answer instantly.

1. What do you call the people who have been invited to take part in a study?

Correct Answer: Correct answer is: (D) Respondents.

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Easy

Concept notes: In the context of sampling, respondents are the individuals who have been invited to participate in a study.

Common Mistakes: A common misunderstanding is confusing respondents with the population involved, which refers to the entire group from which the sample is drawn.

Explanations: Respondents are the specific individuals who have been invited to take part in the study. They are the subset of the population that provides data or information for the research.

Option Analysis:

Option A: Locale of the study refers to the location where the study is conducted, not the people involved.
Option B: Period of the study refers to the time frame during which the study is conducted, not the people involved.
Option C: Population Involved refers to the entire group from which the sample is drawn, not the specific individuals who participate.
Option D: Respondents are the individuals who have been invited to take part in the study.

2. The most important consideration in selecting a sample is that the sample be:

Correct Answer: Correct answer is: (C) Representative of the population.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: The most important consideration in selecting a sample is ensuring that the sample accurately reflects the characteristics of the population from which it is drawn.

Common Mistakes: A common misunderstanding is that a larger sample size or the use of random numbers is the most critical factor, when in fact, representativeness is key.

Explanations: A representative sample ensures that the sample accurately mirrors the population in terms of key characteristics, allowing for valid inferences to be made about the population. This is crucial for the reliability and generalizability of the results.

Option Analysis:

Option A: While random selection can help ensure representativeness, it is not the most important consideration on its own.
Option B: A large number of subjects does not guarantee representativeness; a small, well-chosen sample can be more representative.
Option C: A representative sample is essential for accurate inferences about the population.
Option D: Selecting from a large number of individuals does not ensure representativeness; the sample must reflect the population's characteristics.

Mnemonic: Represents Population

3. In a study of undergraduate students at a university, what is the group of students who are recruited into the study?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: In sampling, the sample is the subset of the population that is actually studied. The population is the entire group of interest, and the sampling frame is the list or method used to identify the population members.

Common Mistakes: A common misunderstanding is confusing the sample with the population. The population includes all members of interest, while the sample is a subset of the population that is actually studied.

Explanations: The group of students recruited into the study is the sample. The sample is a subset of the population that is selected for the study. The population would be all undergraduate students at the university, and the sampling frame would be the method used to identify and recruit these students.

Option Analysis:

Option A: The sampling frame is the method or list used to identify the population members, not the group recruited into the study.
Option B: The population is the entire group of interest, not the subset recruited into the study.
Option C: The sample is the subset of the population that is actually studied, which matches the description of the group recruited into the study.
Option D: This option is incorrect as the sample is the correct term for the group recruited into the study.

Mnemonic: Sample = Subset Studied

4. Allocating equal number of respondents to each subgroup, regardless of size, describes:

Correct Answer: Correct answer is: (B) Disproportionate stratified sampling.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Disproportionate stratified sampling involves allocating an equal number of respondents to each subgroup, regardless of the subgroup's size in the population. This contrasts with proportionate stratified sampling, where the sample size of each subgroup is proportional to the subgroup's size in the population.

Common Mistakes: A common misunderstanding is that proportionate stratified sampling also allocates an equal number of respondents to each subgroup, which is incorrect. Proportionate stratified sampling ensures that the sample reflects the population's subgroup proportions.

Explanations: Disproportionate stratified sampling is the correct answer because it specifically involves allocating an equal number of respondents to each subgroup, regardless of the subgroup's size. This method is used when the researcher wants to ensure that each subgroup is adequately represented in the sample, even if the subgroups are of different sizes in the population.

Option Analysis:

Option A: Proportionate stratified sampling allocates sample sizes proportionally to the subgroup sizes in the population, not equally.
Option B: Disproportionate stratified sampling allocates an equal number of respondents to each subgroup, regardless of the subgroup's size.
Option C: Systematic sampling involves selecting every kth element from a list, not allocating respondents to subgroups.
Option D: Convenience sampling involves selecting individuals based on their availability, not allocating respondents to subgroups.

5. A social work researcher completes a study of students on six college campuses then uses the results to make conclusions about all college students. How is the researcher applying the results?

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

Exam Relevance: AP Statistics, GRE Psychology, Sociology Exams

Difficulty: Moderate

Concept notes: Generalization in research involves applying findings from a specific sample to a broader population.

Common Mistakes: A common misunderstanding is that generalization is only about making broad statements without considering the sample's representativeness.

Explanations: The researcher is applying the results from a study conducted on six college campuses to make conclusions about all college students. This is an example of generalization, where the findings from a specific sample (students on six campuses) are extended to a larger population (all college students).

Option Analysis:

Option A: Correct. The researcher is generalizing the results from a specific sample to a broader population.
Option B: Incorrect. Reduction typically involves simplifying or minimizing the scope of the study, not extending findings to a broader population.
Option C: Incorrect. Abstraction involves removing specific details to focus on general principles, not extending findings to a broader population.
Option D: Incorrect. The correct answer is provided in Option A.

6. What does sampling refer to in research?

Correct Answer: Correct answer is: (B) The process of selecting individuals from the population to participate in the study.

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Easy

Concept notes: Sampling in research refers to the process of selecting a subset of individuals from a larger population to participate in a study. This subset, known as a sample, is used to make inferences about the entire population.

Common Mistakes: A common misunderstanding is that sampling involves analyzing data or publishing results, which are different stages in the research process.

Explanations: Sampling is crucial in research because it allows researchers to make generalizations about a larger population based on the data collected from a smaller, manageable subset. The process of selecting individuals from the population is essential to ensure that the sample is representative and the results are reliable.

Option Analysis:

Option A: This option is incorrect because analyzing data is a different step in the research process, typically occurring after data collection.
Option B: This option is correct because it accurately describes the process of selecting individuals from the population to participate in the study.
Option C: This option is incorrect because publishing research findings is a step that occurs after the data has been analyzed and conclusions have been drawn.
Option D: This option is incorrect because forming a hypothesis is a step that occurs before the sampling process, typically at the beginning of the research design.

7. Mr. Gallagher is conducting a study of college freshmen in Louisiana. He has been able to compile a list of every freshman enrolled in the state supported universities, but the information on students attending private universities is not available to him. The students on his list are referred to as the .....

Correct Answer: Correct answer is: (B) Accessible population.

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

Difficulty: Moderate

Concept notes: In sampling, the accessible population refers to the group of individuals or units that are available and can be reached for the study. It is a subset of the target population, which includes all individuals or units of interest.

Common Mistakes: A common misunderstanding is confusing the accessible population with the target population. The target population includes all individuals of interest, while the accessible population is the subset that can actually be studied.

Explanations: The accessible population is the group of students that Mr. Gallagher can actually study, which includes only those freshmen enrolled in state-supported universities. The information on students attending private universities is not available, so they cannot be included in the study. Therefore, the list of students Mr. Gallagher has compiled is the accessible population.

Option Analysis:

Option A: The target population would include all freshmen in Louisiana, both in state-supported and private universities. Since information on private university students is not available, this is not the correct term.
Option B: The accessible population is the correct term because it refers to the group of students that Mr. Gallagher can actually study, which is limited to those in state-supported universities.
Option C: A sample is a subset of the accessible population that is selected for the study. The list of all freshmen in state-supported universities is not a sample but the accessible population.
Option D: A stratified sample involves dividing the population into subgroups (strata) and then sampling from each subgroup. This is not relevant to the context of the question.

Mnemonic: Accessible = Available and Reachable

8. The correct definition for a sample is:

Correct Answer: Correct answer is: (B) A set of data taken from only part of a population.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In sampling, a sample is a subset of the population that is used to represent the entire population. It is a crucial concept in statistics and research methodology.

Common Mistakes: A common misunderstanding is that a sample must be representative of the entire population, but it is only a subset. Another common mistake is confusing a sample with a census, which involves surveying the entire population.

Explanations: A sample is defined as a subset of the population from which data is collected. It is not a survey of the entire population (Option A), nor does it favor a certain outcome (Option C). It is also not the amount surveyed (Option D). The correct definition is a set of data taken from only part of a population.

Option Analysis:

Option A: This describes a census, not a sample.
Option B: This is the correct definition of a sample.
Option C: This describes a biased sample, not the general definition of a sample.
Option D: This is not a definition of a sample but rather a description of the size of a survey.

9. A teacher samples her class by selecting every third person on her class list. Which type of sampling method is this?

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

Exam Relevance: AP Statistics, IB Mathematics, GRE Quantitative Reasoning

Difficulty: Easy

Concept notes: Systematic sampling involves selecting every kth element from a list or population after a random start. In this case, the teacher selects every third person from the class list.

Common Mistakes: A common misunderstanding is confusing systematic sampling with simple random sampling, where each individual is chosen randomly without a specific pattern.

Explanations: Systematic sampling is a method where every kth element is chosen from a list after a random start. Here, the teacher selects every third person from the class list, which fits the definition of systematic sampling.

Option Analysis:

Option A: Simple random sampling involves selecting individuals completely at random, without any specific pattern. This does not apply here as the teacher is following a specific pattern (every third person).
Option B: Systematic sampling involves selecting every kth element from a list after a random start. This matches the teacher's method of selecting every third person.
Option C: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each subgroup. This does not apply here as the teacher is not dividing the class into subgroups.
Option D: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This does not apply here as the teacher is not selecting entire clusters of students.

10. Identify the sampling technique used in the following study:In an effort to determine customer satisfaction, United Airlines randomly selects 50 flights during a certain week and surveys all passengers on the flights.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters for the study. In this case, the flights represent the clusters, and all passengers on the selected flights are surveyed.

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: United Airlines randomly selects 50 flights, which are the clusters, and surveys all passengers on those flights. This method fits the definition of cluster sampling because the entire clusters (flights) are selected and all members within those clusters (passengers) are included in the study.

Option Analysis:

Option A: Simple Random Sampling (SRS) involves selecting individual members of the population randomly, which is not the case here as entire flights are selected.
Option B: Convenience sampling involves selecting individuals based on ease of access, which is not the case here as flights are randomly selected.
Option C: Systematic sampling involves selecting individuals at regular intervals from a list, which is not the case here as entire flights are selected.
Option D: Cluster sampling involves selecting entire clusters (flights) and surveying all members within those clusters (passengers).
Option E: Stratified sampling involves dividing the population into strata and sampling from each stratum, which is not the case here as entire flights are selected without dividing into strata.

Frequently Asked Questions

What is the difference between a population and a sample in research?

A population includes all members or elements sharing characteristics being studied, while a sample is a subset of the population selected for analysis to make inferences about the population.

How does systematic sampling work?

Systematic sampling involves selecting every kth element from a list after a random start, ensuring a spread of respondents across the population.

What is the purpose of stratified sampling?

Stratified sampling aims to ensure subgroup representation within the sample, improving the accuracy of population inferences by reflecting population characteristics.

Why is random selection important in cluster sampling?

Random selection of clusters in cluster sampling helps ensure that the sample is representative of the population, reducing bias and improving the reliability of the results.

What is the role of accessible population in research?

The accessible population consists of individuals or elements that can be reached and surveyed, making it crucial for practical research design and data collection.

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