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Sampling Quiz 2 (10 MCQs)

This set of multiple-choice questions evaluates understanding of cluster sampling, random selection, and data collection techniques. It covers concepts such as census, cluster sampling, random selection of clusters, and the complete set of population clusters. The material assesses the ability to define population characteristics, determine sample size, and understand the feasibility and accuracy of sampling methods.

Quiz Instructions

Select an option to see the correct answer instantly.

1. According to the text, which of the following is the first step in the sampling design process?

Correct Answer: Correct answer is: (E) Define the population.

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

Difficulty: Easy

Concept notes: The first step in the sampling design process is to define the population from which the sample will be drawn. This ensures that the sample accurately represents the group of interest.

Common Mistakes: A common mistake is to start with selecting a sampling technique or determining the sample size without first clearly defining the population.

Explanations: Defining the population is crucial because it sets the boundaries for the study. It ensures that the sample is drawn from the correct group, which is essential for the validity and reliability of the results. Without a clear definition of the population, the sampling process can lead to biased or irrelevant results.

Option Analysis:

Option A: Counting resources is important but comes after defining the population.
Option B: Determining the sampling frame is a subsequent step after defining the population.
Option C: Selecting sampling techniques is done after defining the population and determining the sampling frame.
Option D: Determining the sample size is a later step in the process, following the definition of the population and selection of sampling techniques.
Option E: Defining the population is the first step in the sampling design process.

2. A principal orders t-shirts and wants to check some of them to make sure they were printed properly. She randomly selects 2 of the 10 boxes of shirts and checks every shirt in those 2 boxes.What type of sampling method is this?

Correct Answer: Correct answer is: (C) Cluster Sampling.

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

Difficulty: Moderate

Concept notes: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters for the sample. In this case, the boxes of shirts represent the clusters.

Common Mistakes: A common mistake 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 principal randomly selects 2 out of the 10 boxes of shirts and checks every shirt in those boxes. This method fits the definition of cluster sampling because the population (all the boxes of shirts) is divided into clusters (the boxes), and entire clusters (the selected boxes) are sampled.

Option Analysis:

Option A: Simple random sampling involves selecting individual items from the population randomly, not entire groups or clusters.
Option B: Stratified sampling involves dividing the population into strata and then sampling from each stratum, which is not what is happening here.
Option C: Cluster sampling involves selecting entire clusters (boxes of shirts) and examining all items within those clusters.
Option D: Systematic sampling involves selecting items from the population at regular intervals, which is not the case here.

3. Which one of the following factors would make a research problem un-researchable?

Correct Answer: Correct answer is: (B) You cannot obtain access to the population of study.

Exam Relevance: GRE, GMAT, Research Methodology Exams

Difficulty: Moderate

Concept notes: In sampling, access to the population is crucial for collecting data. Without access, it is impossible to gather the necessary information, making the research problem un-researchable.

Common Mistakes: A common misunderstanding is that lack of knowledge about the literature or inability to conduct statistical analysis are the primary barriers to research. However, these issues can often be addressed with additional study or resources. Lack of access to the population is a more fundamental issue.

Explanations: Access to the population is essential for sampling. Without this access, researchers cannot collect the necessary data, rendering the research problem unfeasible. The other options, while challenging, do not inherently make the problem un-researchable.

Option Analysis:

Option A: Lack of knowledge about the literature can be addressed by conducting a thorough literature review.
Option B: Without access to the population, it is impossible to collect data, making the research unfeasible.
Option C: Statistical analysis can be learned or outsourced, and does not inherently make the problem un-researchable.
Option D: The inability to add to practice is a limitation but does not make the research unfeasible.

4. Which sampling technique relies on participants' characteristics and not random selection?

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

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

Difficulty: Moderate

Concept notes: Purposive sampling involves selecting participants based on specific characteristics or criteria, rather than through random selection.

Common Mistakes: A common misunderstanding is that random sampling is the only non-biased method, but purposive sampling can be useful when specific characteristics are needed.

Explanations: Purposive sampling relies on the researcher's judgment to select participants who meet certain criteria. This method is not based on random selection but rather on the characteristics of the participants that are relevant to the study. The other sampling techniques, such as random, stratified, and systematic sampling, all involve some form of random selection or systematic approach to ensure a representative sample.

Option Analysis:

Option A: Random sampling involves selecting participants randomly, ensuring each individual has an equal chance of being selected. This does not rely on participants' characteristics.
Option B: Stratified sampling involves dividing the population into subgroups (strata) and then randomly selecting participants from each subgroup. This method still involves random selection within strata.
Option C: Systematic sampling involves selecting participants at regular intervals from a list or sequence. This method is systematic but still involves a form of random selection.
Option D: Purposive sampling involves selecting participants based on specific characteristics or criteria, not random selection.

5. All the people with the characteristics that a researcher wants to study.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: In sampling, the population refers to the complete set of individuals or items that share characteristics being studied.

Common Mistakes: A common misunderstanding is confusing the population with a sample, which is a subset of the population used for analysis.

Explanations: The population in sampling is the entire group of individuals or items that have the characteristics the researcher is interested in studying. This is the complete set from which a sample is drawn for analysis. The term "population" accurately describes all the people or items with the desired characteristics.

Option Analysis:

Option A: Correct. The population is the complete set of individuals or items with the characteristics being studied.
Option B: Incorrect. A survey is a method of collecting data from a sample of the population, not the population itself.
Option C: Incorrect. A questionnaire is a tool used to collect data from individuals, not the population itself.
Option D: Incorrect. "Boat Edit" is not a relevant term in the context of sampling.

6. Data collected from each and every unit of population is called ..... method

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

Exam Relevance: AP Statistics, GRE, GMAT, Census Bureau exams

Difficulty: Easy

Concept notes: Census refers to the process of collecting data from every unit in a population.

Common Mistakes: A common mistake is confusing census with sampling, where only a subset of the population is surveyed.

Explanations: Census involves collecting data from every unit in the population, which aligns with the definition provided in the question. Sampling, on the other hand, involves collecting data from a subset of the population, not every unit.

Option Analysis:

Option A: Sampling involves collecting data from a subset of the population, not every unit.
Option B: Census involves collecting data from every unit in the population, which matches the question's description.
Option C: Data collection is a general term and does not specify whether it is from every unit or a subset.
Option D: Research design refers to the overall plan for conducting research, not specifically to data collection from every unit.

7. You must survey schools in a state. You randomly select schools and then survey every student in those schools. Which method is this?

Correct Answer: Correct answer is: (B) One-stage cluster sampling using schools.

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. One-stage cluster sampling means that all members of the selected clusters are included in the sample.

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: In this scenario, the population of interest is the students in the state. The schools are treated as clusters, and a random selection of schools is made. Then, every student within the selected schools is surveyed. This method fits the definition of one-stage cluster sampling because the entire cluster (school) is included in the sample.

Option Analysis:

Option A: Systematic sampling by class roster involves selecting every nth student from a list, which is not the case here.
Option B: One-stage cluster sampling using schools is correct because the entire school (cluster) is included in the sample.
Option C: Two-stage cluster sampling involves an additional stage of sampling within the selected clusters, which is not described in the scenario.
Option D: Stratified sampling by grade level involves dividing the population into strata (grades) and sampling from each stratum, which is not the method used here.

8. How many people were polled in this survey?

Correct Answer: Correct answer is: (D) 145 people.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In sampling, the total number of people polled is a key piece of information. This question requires identifying the total sample size from the given options.

Common Mistakes: A common mistake is to misinterpret the options or overlook the total number of people polled, leading to incorrect selection of a smaller number.

Explanations: The correct answer is 145 people because the question asks for the total number of people polled in the survey. The other options (5, 40, and 100) are smaller and do not represent the total sample size.

Option Analysis:

Option A: 5 people is too small to be the total number of people polled in a survey.
Option B: 40 people is also too small to be the total number of people polled in a survey.
Option C: 100 people is still too small to be the total number of people polled in a survey.
Option D: 145 people is the correct total number of people polled in the survey.

9. What do representative samples accurately reflect?

Correct Answer: Correct answer is: (A) The characteristics of the population.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A representative sample is designed to accurately reflect the characteristics of the population from which it is drawn.

Common Mistakes: A common misunderstanding is that a representative sample reflects the opinions of the researchers or the preferences of the sample collectors, rather than the actual characteristics of the population.

Explanations: A representative sample is a subset of a population that accurately reflects the characteristics of the entire population. This ensures that the sample can be used to make valid inferences about the population. The goal of sampling is to ensure that the sample is representative, so that the results obtained from the sample can be generalized to the population.

Option Analysis:

Option A: Correct. A representative sample accurately reflects the characteristics of the population.
Option B: Incorrect. The sample should not reflect the opinions of the researchers.
Option C: Incorrect. The sample should not be influenced by the results of previous studies.
Option D: Incorrect. The sample should not reflect the preferences of the sample collectors.

10. Interview the first 30 students who enter the school in the morning. What type of sample is this?

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

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

Difficulty: Moderate

Concept notes: Convenience sampling involves selecting individuals who are easiest to reach or most readily available. This method is often used when the researcher needs quick and easy access to participants.

Common Mistakes: A common misunderstanding is to confuse convenience sampling with simple random sampling, where every individual has an equal chance of being selected. In this case, the first 30 students entering the school are not randomly chosen but are simply the most accessible.

Explanations: The method described involves interviewing the first 30 students who enter the school in the morning. This approach is a form of convenience sampling because it relies on the ease of access to these students rather than a random selection process. The students are not chosen based on any specific criteria or random selection, but rather because they are the first to arrive, making them the most convenient to interview.

Option Analysis:

Option A: Simple random sampling requires that every individual in the population has an equal chance of being selected, which is not the case here.
Option B: Voluntary response sampling involves individuals self-selecting to participate, which is not the case here as the students are not volunteering.
Option C: Systematic sampling involves selecting individuals at regular intervals from a list or sequence, which is not the case here.
Option D: Convenience sampling involves selecting individuals who are easiest to reach, which fits the scenario described.

Frequently Asked Questions

What is the main difference between census and sampling?

A census collects data from every member of a population, while sampling involves selecting a subset of the population to study, which is more practical and cost-effective.

How does cluster sampling work?

Cluster sampling involves dividing the population into clusters, randomly selecting some of these clusters, and then studying all members within the selected clusters.

What is the purpose of one-stage cluster sampling?

One-stage cluster sampling simplifies data collection by selecting entire clusters at once, making it easier to manage and more feasible when studying large populations.

How does purposive sampling differ from random selection?

Purposive sampling involves non-random selection based on specific characteristics, while random selection ensures every member of the population has an equal chance of being included.

Why is accessibility important in sampling?

Accessibility ensures that researchers can reach and study the population effectively, which is crucial for obtaining accurate and representative data.

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