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Sampling Quiz 17 (10 MCQs)

This set of multiple-choice questions evaluates understanding of sampling methods, including stratified sampling, non-probability sampling, and judgemental sampling. It assesses the ability to define and identify populations, determine sample sizes, and understand the implications of sampling bias and representation in research.

Quiz Instructions

Select an option to see the correct answer instantly.

1. The school librarian wants to determine how many students use the library on a regular basis. What type of sampling method would she use if she chose to randomly select 20 students in the cafeteria during each of the three lunch periods on Monday.

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

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

Difficulty: Moderate

Concept notes: A stratified random sample involves dividing the population into distinct subgroups (strata) and then randomly selecting samples from each subgroup. This ensures that each subgroup is represented in the sample.

Common Mistakes: A common mistake is confusing stratified random sampling with simple random sampling, where every individual in the population has an equal chance of being selected without any subgroup division.

Explanations: The librarian divides the students into three strata based on lunch periods and then randomly selects 20 students from each stratum. This method ensures that each lunch period is represented in the sample, making it a stratified random sample.

Option Analysis:

Option A: A convenience sample involves selecting individuals who are easiest to reach, which does not apply here as the librarian is not choosing students based on convenience.
Option B: A simple random sample involves selecting individuals randomly from the entire population without any subgroup division, which is not the case here.
Option C: A stratified random sample involves dividing the population into strata and then randomly selecting from each stratum, which matches the librarian's method.
Option D: An interval sample involves selecting every nth individual from a list, which is not the method used here.

2. This occurs when the sample is not adequate for the aims of the research.

Correct Answer: Correct answer is: (B) Sampling bias.

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Moderate

Concept notes: Sampling bias occurs when the sample used in a study is not representative of the population, leading to skewed or inaccurate results.

Common Mistakes: A common misunderstanding is confusing sampling bias with other types of biases, such as confirmation bias or question order bias, which are unrelated to the sample selection process.

Explanations: Sampling bias occurs when the sample is not adequate for the aims of the research, meaning the sample does not accurately reflect the population being studied. This can lead to results that are not generalizable or representative of the broader population.

Option Analysis:

Option A: Confirmation bias is the tendency to favor information that confirms one's preconceptions or hypotheses, which is unrelated to the adequacy of the sample.
Option B: Sampling bias is the correct answer because it directly addresses the issue of the sample not being adequate for the research aims.
Option C: Question order bias refers to the effect of the order in which questions are asked on the responses, which is not related to the adequacy of the sample.
Option D: Biased reporting refers to the way results are presented, which is not directly related to the adequacy of the sample.

3. What is a sampling procedure wherein the researcher chooses his/her own respondents based on his/her expert opinion?

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

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Moderate

Concept notes: Judgemental sampling is a non-probability sampling technique where the researcher selects the sample based on their own judgement and expertise. This method relies heavily on the researcher's discretion and experience to choose the most appropriate participants for the study.

Common Mistakes: A common misunderstanding is confusing judgemental sampling with convenience sampling, where participants are chosen based on ease of access rather than the researcher's expertise.

Explanations: Judgemental sampling involves the researcher using their expert opinion to select participants who are most suitable for the study. This method is often used when the researcher has specific criteria in mind and believes they can identify the most appropriate participants based on their knowledge and experience.

Option Analysis:

Option A: Convenience sampling involves selecting participants based on their availability and ease of access, not the researcher's expertise.
Option B: Judgemental sampling involves the researcher's expert opinion in selecting participants, which aligns with the question's description.
Option C: Snowball sampling involves existing study subjects recruiting future subjects from among their acquaintances, which does not involve the researcher's expert opinion.
Option D: Systematic sampling involves selecting every nth element from a list, which is a structured and non-discretionary method.

Mnemonic: JUDGE: Judgemental sampling relies on the researcher's expert JUDGEment.

4. When considering the food preferences of students in his Data Management class at their high school, the teacher decides to ask every student in the class what they like to eat. What is the population for this question?

Correct Answer: Correct answer is: (A) The students in the Data Management class.

Exam Relevance: AP Statistics, IB Mathematics, A-Level Statistics

Difficulty: Easy

Concept notes: In sampling, the population is the complete set of individuals or items that are the subject of study. Here, the teacher is interested in the food preferences of students in his Data Management class, so the population is the students in that specific class.

Common Mistakes: A common mistake is to assume the population is broader than the specific group being studied, such as all students at the high school or all students taking math.

Explanations: The population for this question is the students in the Data Management class because the teacher is specifically asking about the food preferences of these students. The other options (students taking math, students in Grade 12, or all students at the high school) are too broad and include students who are not part of the Data Management class.

Option Analysis:

Option A: This is the correct answer because the population is the specific group of students in the Data Management class.
Option B: This is incorrect because it includes all students taking math, which is a broader group than just the Data Management class.
Option C: This is incorrect because it includes all Grade 12 students, which is a broader group than just the Data Management class.
Option D: This is incorrect because it includes all students at the high school, which is a broader group than just the Data Management class.

5. Subdivisions of a population are called:

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In sampling, a subdivision of a population is called a stratum. This is a key concept in stratified sampling, where the population is divided into distinct, non-overlapping subgroups (strata) based on specific characteristics.

Common Mistakes: A common misunderstanding is to confuse "strata" with "groups," which is a more general term and not specific to sampling techniques.

Explanations: In the context of sampling, a population is often divided into distinct subgroups called strata. Each stratum is homogeneous within itself but heterogeneous between different strata. This allows for more precise sampling and analysis by ensuring that each subgroup is adequately represented.

Option Analysis:

Option A: "Groups" is a general term and not specific to sampling techniques.
Option B: "Strata" is the correct term for subdivisions in sampling.
Option C: "Bias" refers to systematic errors in sampling, not subdivisions.
Option D: "None of the above" is incorrect as "strata" is the correct term.

6. How many total people were surveyed about what ice cream flavor they would pick?

Correct Answer: Correct answer is: (D) 269.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In sampling, the total number of people surveyed is the sum of all responses collected. This question requires summing up the responses to determine the total sample size.

Common Mistakes: A common mistake is to misinterpret the question and only consider a subset of the responses or to miscount the total number of responses.

Explanations: To find the total number of people surveyed, we need to sum up all the responses. The problem states that the total number of people surveyed is 269. This means that the sum of all individual responses (regardless of the ice cream flavor) equals 269. Therefore, the correct answer is 269.

Option Analysis:

Option A: 107 is incorrect because it does not represent the total number of people surveyed.
Option B: 92 is incorrect because it does not represent the total number of people surveyed.
Option C: 70 is incorrect because it does not represent the total number of people surveyed.
Option D: 269 is correct because it represents the total number of people surveyed.

7. Dr. Alee is interested in the prevalence of ADHD among five-year-old boys. The population in Dr. Alee's research is

Correct Answer: Correct answer is: (A) All five-year-old boys.

Exam Relevance: AP Statistics, GRE, MCAT, Psychology exams

Difficulty: Moderate

Concept notes: In sampling, the population refers to the entire group of individuals or items that are the subject of a study. The population must include all members or elements that are being studied.

Common Mistakes: A common mistake is to confuse the population with a subset of the population, such as only those diagnosed with ADHD, rather than the entire group of interest.

Explanations: The population in Dr. Alee's research is all five-year-old boys because the study aims to determine the prevalence of ADHD among this specific age and gender group. The population must include all five-year-old boys, not just those diagnosed with ADHD or a broader group of children or people.

Option Analysis:

Option A: Correct. This option correctly identifies the entire group of five-year-old boys as the population.
Option B: Incorrect. This option only includes a subset of the population (those diagnosed with ADHD), not the entire group of five-year-old boys.
Option C: Incorrect. This option includes a broader group (all children diagnosed with ADHD) rather than the specific group of interest (five-year-old boys).
Option D: Incorrect. This option includes an even broader group (all people diagnosed with ADHD) rather than the specific group of interest (five-year-old boys).

8. A "good" sample is said to have which of the following characteristics?

Correct Answer: Correct answer is: (D) All of the above.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: A "good" sample in sampling should have characteristics that allow for accurate representation and reliable statistical inference.

Common Mistakes: A common misunderstanding is that a "good" sample only needs to be representative, without considering the other aspects such as probability, sample size, and confidence levels.

Explanations: A "good" sample should identify the probability that a unit of analysis will be included in the study, which ensures that the sample is representative and unbiased. It should also enable decisions concerning the sample size requirement, ensuring that the sample is large enough to provide reliable estimates. Additionally, a "good" sample should enable the quantification of the degree of confidence made from inferential statistics, which allows for accurate conclusions to be drawn from the sample data. Therefore, all of the above characteristics are essential for a "good" sample.

Option Analysis:

Option A: Identifies the probability that a unit of analysis will be included in the study. This is a key characteristic of a "good" sample as it ensures representativeness and reduces bias.
Option B: Enables decisions concerning sample size requirement. This is important to ensure the sample is large enough to provide reliable estimates.
Option C: Enables quantification of the degree of confidence made from inferential statistics. This is crucial for making accurate conclusions from the sample data.
Option D: All of the above. This option correctly identifies that all the listed characteristics are essential for a "good" sample.

9. Subset of a population chosen for inclusion in an experiment

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A sample is a subset of a population chosen for inclusion in an experiment or study. It is used to make inferences about the larger population.

Common Mistakes: A common misunderstanding is confusing a sample with the entire population. A sample is only a part of the population, not the whole.

Explanations: In sampling, a subset of a population is selected to represent the entire population. This subset is called a sample. The purpose of selecting a sample is to make inferences about the population based on the data collected from the sample. Therefore, the correct term for a subset of a population chosen for inclusion in an experiment is a sample.

Option Analysis:

Option A: A case study is an in-depth examination of a particular instance or situation, not a subset of a population.
Option B: Observations refer to the act of watching and recording data, not a subset of a population.
Option C: A sample is a subset of a population chosen for inclusion in an experiment.
Option D: This option is incorrect as "Sample" is the correct term.

Mnemonic: S-P: Sample is a Part of the Population.

10. A researcher puts an advert in a newspaper, asking for people to take part in their study on mental health. Which sampling technique have they used?

Correct Answer: Correct answer is: (B) Volunteer sampling.

Exam Relevance: AP Statistics, IB Psychology, Research Methods in Psychology

Difficulty: Easy

Concept notes: Volunteer sampling is a non-probability sampling technique where participants volunteer to take part in the study.

Common Mistakes: A common misunderstanding is that volunteer sampling is a form of random sampling, but it is not. Participants are self-selected, which can introduce bias.

Explanations: The researcher placed an advert in a newspaper asking for people to take part in the study. This method relies on individuals who choose to volunteer, which aligns with the definition of volunteer sampling. In volunteer sampling, participants are not randomly selected but rather self-select into the study, which can lead to a non-representative sample.

Option Analysis:

Option A: Stratified sampling involves dividing the population into subgroups (strata) and then randomly selecting samples from each subgroup. This is not applicable here as the participants are not selected from predefined strata.
Option B: Volunteer sampling is the correct choice because the participants are self-selected through the newspaper advert.
Option C: Opportunity sampling involves selecting participants based on their availability and willingness to participate at the time of the study. While similar, volunteer sampling specifically refers to participants who respond to a call for volunteers.
Option D: Random sampling involves selecting participants randomly from the entire population, which is not the case here as participants are self-selected.
Option E: Systematic sampling involves selecting participants at regular intervals from a list or sequence, which is not the case here as participants are self-selected.

Frequently Asked Questions

What is the difference between probability and non-probability sampling?

Probability sampling involves selecting participants randomly, ensuring each member of the population has a known chance of being included. Non-probability sampling relies on the researcher's discretion, where participants are chosen based on specific criteria or convenience.

How does stratified random sampling work?

Stratified random sampling divides the population into subgroups (strata) based on shared characteristics, then randomly selects samples from each stratum to ensure representation from all segments of the population.

What is sampling bias and how can it be minimized?

Sampling bias occurs when certain members of a population are more likely to be selected than others, leading to skewed results. It can be minimized by using random sampling techniques and ensuring the sample is representative of the population.

Why is defining the population important in sampling?

Defining the population clearly ensures that the sample accurately represents the group being studied, which is crucial for the validity and reliability of the research findings.

What is the role of sample size in research?

Sample size affects the precision and reliability of research findings. A larger sample size generally reduces sampling error and increases the confidence in the results.

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