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Sampling Quiz 58 (10 MCQs)

This set of multiple-choice questions evaluates understanding of sampling techniques, including random sampling, stratified sampling, and systematic sampling. It tests knowledge of population vs. sample, representativeness, sampling bias, and the importance of sample size and selection methods. Concepts such as availability, convenience sampling, and non-probability sampling are also covered.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Respondents are obtained on the availability or preference of the researcher

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

Exam Relevance: AP Statistics, GRE, MCAT, GMAT

Difficulty: Easy

Concept notes: Convenience sampling involves selecting individuals based on their availability and ease of access to the researcher.

Common Mistakes: A common misunderstanding is that convenience sampling is a random method, but it is not. It relies on the ease of access rather than a systematic or random selection process.

Explanations: Convenience sampling is a non-probability sampling technique where participants are selected based on their availability and ease of access. This method is often used when the researcher can easily obtain data from individuals who are readily available, making it a convenient choice. The other sampling methods listed do not fit the description of selecting respondents based on availability or preference of the researcher.

Option Analysis:

Option A: Correct. Convenience sampling involves selecting individuals based on their availability and ease of access to the researcher.
Option B: Incorrect. Purposive sampling involves selecting individuals based on specific characteristics or qualities, not availability.
Option C: Incorrect. Quota sampling involves selecting individuals to meet specific quotas, not based on availability.
Option D: Incorrect. Voluntary sampling involves individuals who volunteer to participate, not necessarily based on availability.
Option E: Incorrect. Snowball sampling involves existing study subjects recruiting future subjects from among their acquaintances, not based on availability.

2. How is random sampling helpful?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT, DAT

Difficulty: Moderate

Concept notes: Random sampling is a method of selecting a subset of individuals from a population to estimate characteristics of the whole population. It is widely used in statistics and research due to its benefits.

Common Mistakes: A common misunderstanding is that random sampling is only useful for ensuring accuracy, but it also offers economic benefits and reduces personal biases.

Explanations: Random sampling is helpful because it is reasonably accurate, as it provides a representative subset of the population. It is also an economical method of data collection, as it requires fewer resources compared to surveying the entire population. Additionally, random sampling is free from personal biases, as each individual has an equal chance of being selected, ensuring that the sample is not skewed by the researcher's preferences or preconceptions.

Option Analysis:

Option A: Random sampling is reasonably accurate because it provides a representative subset of the population, which can be used to make inferences about the whole population.
Option B: Random sampling is an economical method of data collection because it requires fewer resources compared to surveying the entire population.
Option C: Random sampling is free from personal biases because each individual has an equal chance of being selected, ensuring that the sample is not skewed by the researcher's preferences or preconceptions.
Option D: All of the above statements are true, making this the correct answer.

Mnemonic: RAND: Random, Accurate, Not biased, Data-efficient

3. Sample ..... means the number of items to be selected from the universe to constitute a sample.

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

Exam Relevance: AP Statistics, GRE, GMAT, MBA Entrance Exams

Difficulty: Easy

Concept notes: In sampling, the "size" of a sample refers to the number of items or observations selected from the population or universe.

Common Mistakes: A common misunderstanding is confusing "size" with other sampling terms like "unit" or "method."

Explanations: The term "size" in sampling directly refers to the number of items selected from the population. This is a fundamental concept in sampling theory, where the sample size is crucial for determining the representativeness and reliability of the sample.

Option Analysis:

Option A: Correct. The size of a sample is the number of items selected from the population.
Option B: Incorrect. The unit refers to the individual items or elements in the population, not the number of items selected.
Option C: Incorrect. The method refers to the technique used to select the sample, not the number of items selected.
Option D: Incorrect. The design refers to the overall plan for selecting the sample, not the number of items selected.

4. A method for choosing the sample for the research study in which participants are selected form a variety of levels or types of people in the population.

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

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

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) based on specific characteristics and then selecting samples from each subgroup. This ensures that the sample is representative of the entire population.

Common Mistakes: A common misunderstanding is confusing stratified sampling with random sampling, where participants are chosen randomly without considering specific subgroups.

Explanations: Stratified sampling is the correct method because it involves selecting participants from various levels or types of people in the population, ensuring that each subgroup is adequately represented. This method is particularly useful when the population has distinct subgroups that need to be represented proportionally in the sample.

Option Analysis:

Option A: Random sample involves selecting participants randomly from the entire population without considering subgroups. This does not ensure representation from various levels or types of people.
Option B: Statistical sample is a general term and does not specify the method of selection. It does not necessarily involve selecting from various levels or types of people.
Option C: Stratified sample involves dividing the population into subgroups and selecting samples from each subgroup, ensuring representation from various levels or types of people.
Option D: Quasi-sample is not a standard sampling method and does not describe the process of selecting participants from various levels or types of people.

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

5. The difference between a statistical average based on the entire population and the one based on a sample is known as

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Sampling error is the difference between a statistical average based on the entire population and the one based on a sample.

Common Mistakes: A common misunderstanding is confusing sampling error with standard error, which is the standard deviation of the sampling distribution of a statistic.

Explanations: Sampling error occurs because a sample may not perfectly represent the entire population. The difference between the sample statistic and the population parameter is known as the sampling error. This error arises due to the variability inherent in selecting a subset of the population rather than measuring the entire population.

Option Analysis:

Option A: Standard Error is the standard deviation of the sampling distribution of a statistic, not the difference between a sample and population average.
Option B: Mean Difference is the difference between the means of two groups, not the difference between a sample and population average.
Option C: Sampling Error is the correct term for the difference between a statistical average based on the entire population and the one based on a sample.
Option D: Mean Deviation is the average of the absolute differences between each data point and the mean, not the difference between a sample and population average.

6. A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. This is an example of a

Correct Answer: Correct answer is: (B) Convenience sample.

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

Difficulty: Easy

Concept notes: A convenience sample is a type of non-probability sampling where the sample is selected based on ease of access and availability. The sportswriter chose to interview the first 20 people who entered the stadium, which is a convenient and easily accessible group.

Common Mistakes: A common misunderstanding is to confuse a convenience sample with a random sample. A random sample involves selecting participants randomly from the entire population, whereas a convenience sample involves selecting participants based on their availability and ease of access.

Explanations: The sportswriter chose to interview the first 20 people who entered the stadium, which is a convenient and easily accessible group. This method of sampling is known as a convenience sample because it relies on the ease of access to the participants rather than a systematic or random selection process.

Option Analysis:

Option A: A cluster sample involves dividing the population into clusters and then randomly selecting entire clusters for the sample. This is not the case here as the sportswriter did not divide the population into clusters.
Option B: A convenience sample involves selecting participants based on their availability and ease of access. This is the correct choice as the sportswriter interviewed the first 20 people who entered the stadium.
Option C: A voluntary response sample involves participants who choose to respond to a survey or participate in a study. This is not the case here as the sportswriter selected the participants rather than the participants choosing to be part of the sample.
Option D: A stratified random sample involves dividing the population into strata and then randomly selecting participants from each stratum. This is not the case here as the sportswriter did not divide the population into strata.

Mnemonic: Convenience = Conveniently Available

7. A SURVEY OF 500 ADULTS IN THE U.S. FOUND THAT 54% DRINK COFEE DAILY. IDENTIFY THE POPULATION

Correct Answer: Correct answer is: (B) COLLECTION OF ALL ADULTS IN THE U.S.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In sampling, the population refers to the entire group of individuals or items that are the subject of the study. The sample is a subset of the population used to make inferences about the population.

Common Mistakes: A common mistake is to confuse the sample with the population. The sample is the group that is actually surveyed, while the population is the larger group that the sample is meant to represent.

Explanations: The population in this context is the entire group of adults in the U.S. The survey of 500 adults is a sample taken from this larger population. The goal of the survey is to make inferences about the coffee-drinking habits of all adults in the U.S. based on the responses of the 500 surveyed adults.

Option Analysis:

Option A: This option refers to the sample, not the population. The sample is the 500 adults surveyed, but the population is the entire group of adults in the U.S.
Option B: This option correctly identifies the population as the collection of all adults in the U.S.
Option C: This option refers to the percentage of adults who drink coffee daily, which is a statistic derived from the sample, not the population itself.
Option D: This option refers to the sample size, which is 500 adults, not the population.

8. Sampling bias results in a sample that is not .....

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Sampling bias occurs when a sample is not representative of the population from which it is drawn. This means that the sample does not accurately reflect the characteristics of the entire population.

Common Mistakes: A common misunderstanding is that sampling bias only affects the accessibility or selection process of the sample, rather than its representativeness.

Explanations: Sampling bias results in a sample that is not representative. A representative sample accurately reflects the characteristics of the population, ensuring that the sample is a true reflection of the whole. If a sample is biased, it means that certain characteristics are overrepresented or underrepresented, leading to skewed results that do not accurately reflect the population.

Option Analysis:

Option A: This option is incorrect because sampling bias does not imply that the sample is not selected from a population. It means the sample is not representative of the population.
Option B: This option is incorrect because sampling bias does not affect the accessibility of the sample. It affects the representativeness of the sample.
Option C: This option is incorrect because the term "biased" is already used to describe the issue, and stating that the sample is not "biased" would be contradictory.
Option D: This option is correct because sampling bias results in a sample that is not representative of the population.

9. Marshall intends to collect a systematic sample of 300 people in a population of 6000. He/she numbers each element of the population from 1-6000 and will choose every ..... individual to be a part of the sample.

Correct Answer: Correct answer is: (C) 20th.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: In systematic sampling, a sample is chosen by selecting every kth element from a list of the population. The value of k is determined by dividing the total population size by the desired sample size.

Common Mistakes: A common mistake is to misinterpret the calculation of k, leading to incorrect intervals for selecting the sample.

Explanations: To determine the interval (k) for systematic sampling, we use the formula: \[ k = \frac{\text{Total Population Size}}{\text{Sample Size}} \] Given the total population size is 6000 and the sample size is 300, we calculate: \[ k = \frac{6000}{300} = 20 \] Thus, Marshall will choose every 20th individual to be part of the sample.

Option Analysis:

Option A: 10th. This would result in a sample size of 600, which is incorrect.
Option B: 200th. This would result in a sample size of 30, which is incorrect.
Option C: 20th. This is the correct interval as it results in a sample size of 300.
Option D: 31st. This would result in a sample size of approximately 193, which is incorrect.

10. What is Volunteer Bias?

Correct Answer: Correct answer is: (D) People who volunteer for research differ systematically from those who do not.

Exam Relevance: AP Statistics, GRE Psychology, MCAT

Difficulty: Moderate

Concept notes: Volunteer bias occurs when the individuals who choose to participate in a study differ in significant ways from those who do not volunteer. This can lead to skewed results that do not accurately represent the broader population.

Common Mistakes: A common misunderstanding is that volunteer bias only affects the sample size, when in fact it affects the representativeness of the sample.

Explanations: Volunteer bias is a type of selection bias that arises when the volunteers for a study are not representative of the population of interest. This can happen because volunteers may have different characteristics, motivations, or experiences compared to non-volunteers. For example, volunteers might be more health-conscious, more interested in the topic of the study, or more available to participate. These differences can lead to biased results that do not generalize to the broader population.

Option Analysis:

Option A: This describes experimenter bias, where the researcher's expectations influence participants' behavior.
Option B: This describes dominance bias, where one or two individuals dominate a focus group discussion.
Option C: This describes response bias, where participants tend to respond in a certain way regardless of the question.
Option D: This correctly describes volunteer bias, where volunteers differ systematically from non-volunteers.

Frequently Asked Questions

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

A population includes all members or items for analysis, while a sample is a subset of the population used to represent the whole group. Researchers often use samples to make inferences about the population.

How does random sampling help in reducing bias?

Random sampling ensures that every member of the population has an equal chance of being selected, which helps to minimize selection bias and provides a more representative sample of the population.

What is the purpose of stratified sampling?

Stratified sampling involves dividing the population into subgroups (strata) based on specific characteristics and then sampling from each subgroup. This method ensures that all subgroups are represented in the sample, improving the accuracy of the results.

What is the role of sample size in research?

Sample size affects the precision and reliability of research findings. Larger sample sizes generally provide more accurate estimates of population parameters and reduce sampling error.

How does convenience sampling differ from random sampling?

Convenience sampling involves selecting individuals who are easiest to reach, while random sampling ensures each member of the population has an equal chance of being selected. Convenience sampling can introduce bias, whereas random sampling aims to be unbiased.

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