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Probability Sampling Quiz 15 (10 MCQs)

This set of multiple-choice questions evaluates understanding of systematic sampling, fixed interval selection, and other probability sampling methods. It tests knowledge of random selection, equal probability, and the creation of representative samples. Concepts such as stratified random sampling, simple random sampling, and the use of random number generation are also covered.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Each participant is randomly selected from the target population. Every member of the group has an equal chance of being selected (e.g. the names of every member of the group is put in a hat and the required number of names is picked out.

Correct Answer: Correct answer is: (B) Random Sampling Technique.

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

Difficulty: Easy

Concept notes: Random sampling is a probability sampling technique where each member of the population has an equal chance of being selected.

Common Mistakes: A common misunderstanding is confusing random sampling with other sampling techniques like convenience sampling, where participants are selected based on ease of access rather than equal probability.

Explanations: In random sampling, every member of the target population has an equal chance of being selected. This ensures that the sample is representative of the population, reducing bias. The described method of putting names in a hat and picking them out is a simple example of random sampling.

Option Analysis:

Option A: Opportunity Sampling Technique involves selecting participants based on convenience or availability, not equal probability.
Option B: Random Sampling Technique ensures each member of the population has an equal chance of being selected, matching the description.
Option C: Volunteer Sampling Technique involves participants who volunteer, which can introduce bias and does not ensure equal probability.
Option D: None of the above is incorrect as the described method fits the definition of random sampling.

2. This procedure allows every member of the targeted population an equal chance of being selected for the study.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Random sampling is a probability sampling technique where every member of the population has an equal chance of being selected.

Common Mistakes: A common misunderstanding is that other sampling methods, such as convenience or quota sampling, also provide an equal chance of selection for all members of the population.

Explanations: Random sampling ensures that each member of the population has an equal probability of being included in the sample. This method minimizes bias and ensures that the sample is representative of the entire population.

Option Analysis:

Option A: Correct. Random sampling ensures every member of the population has an equal chance of being selected.
Option B: Incorrect. Quota sampling involves selecting participants based on specific characteristics, not equal chance.
Option C: Incorrect. Convenience sampling selects participants based on ease of access, not equal chance.
Option D: Incorrect. Snowball sampling relies on referrals from initial participants, not equal chance.

3. At a police sobriety checkpoint, every fifth driver was stopped and interviewed by the local police department.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a population after a random start. In this case, every fifth driver is stopped, which fits the definition of systematic sampling.

Common Mistakes: A common mistake is confusing systematic sampling with random sampling. While systematic sampling involves a fixed interval, random sampling does not follow a specific pattern.

Explanations: In systematic sampling, a fixed interval (k) is used to select elements from a population. Here, every fifth driver is stopped, indicating a fixed interval of 5. This method ensures that the sample is spread evenly throughout the population, which is a characteristic of systematic sampling.

Option Analysis:

Option A: Random sampling involves selecting elements from a population randomly, without any specific pattern. This does not apply here as every fifth driver is stopped, which is a fixed interval.
Option B: Systematic sampling involves selecting every kth element from a population after a random start. This matches the scenario where every fifth driver is stopped.
Option C: Convenience sampling involves selecting elements based on ease of access, which is not the case here as there is a fixed interval.
Option D: Stratified sampling involves dividing the population into subgroups and then sampling from each subgroup. This does not apply as there is no mention of subgroups.
Option E: Cluster sampling involves dividing the population into clusters and then sampling entire clusters. This does not apply as individual drivers are being sampled, not clusters of drivers.

4. A researcher divides the populations into PG, graduates and 10+2 students and using the random digit table he selects some of them from each. This is technically called.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified random sampling is a method of probability sampling where the population is divided into distinct subgroups (strata) based on certain characteristics, and then random samples are drawn from each stratum.

Common Mistakes: A common misunderstanding is confusing stratified random sampling with simple random sampling, where the entire population is treated as a single group without any division.

Explanations: In the given scenario, the researcher divides the population into distinct subgroups (PG, graduates, and 10+2 students) and then selects some individuals from each subgroup using a random digit table. This method ensures that each subgroup is represented in the sample, which is the essence of stratified random sampling.

Option Analysis:

Option A: Settled sampling is not a recognized term in probability sampling methods.
Option B: Stratified random sampling is the correct method as it involves dividing the population into strata and then randomly selecting samples from each stratum.
Option C: Representative sampling is a general term and does not specify the method of dividing the population into strata.
Option D: None of these is incorrect because stratified random sampling is a valid method.

5. Which category of sampling is used when the probability of selecting each individual in a population is known and every member of the population has an equal chance of being selected?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Probability sampling is a method where each member of the population has a known, non-zero probability of being selected. This ensures that every individual has an equal chance of being included in the sample.

Common Mistakes: A common misunderstanding is that nonprobability sampling also ensures equal chances of selection, but in nonprobability sampling, the probability of selection is not known or equal.

Explanations: Probability sampling is the correct answer because it involves selecting individuals from a population in such a way that each individual has a known, non-zero probability of being chosen. This ensures that the sample is representative of the population and reduces bias.

Option Analysis:

Option A: Correct. Probability sampling ensures each individual has a known and equal chance of being selected.
Option B: Incorrect. Nonprobability sampling does not ensure that each individual has an equal chance of being selected.
Option C: Incorrect. Only probability sampling ensures equal chances of selection.
Option D: Incorrect. Probability sampling is the correct method for ensuring equal chances of selection.

6. A hospital selects every 5th patient for a satisfaction survey. What is the key step that makes this systematic?

Correct Answer: Correct answer is: (A) Using a fixed interval after a random start.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a population after a random start. This method ensures a spread of samples across the entire population.

Common Mistakes: A common misunderstanding is that systematic sampling requires matching or equal distribution, which is not the case. It relies on a fixed interval and a random starting point.

Explanations: Systematic sampling is characterized by selecting every kth element from a population after a random start. In this case, the hospital selects every 5th patient, which fits the definition of systematic sampling. The key step is using a fixed interval (every 5th patient) after a random start, ensuring a representative sample.

Option Analysis:

Option A: This is the correct answer as it describes the key step in systematic sampling.
Option B: Matching patients by similar diagnoses is not a characteristic of systematic sampling.
Option C: Including all patients arriving on weekends does not follow the systematic sampling method.
Option D: Ensuring equal numbers from each ward is not a requirement for systematic sampling.

7. Select three students from a class to receive ice cream by putting all the students' names in a hat and picking out three names randomly.

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

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

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 selected.

Common Mistakes: A common misunderstanding is confusing simple random sampling with other types of probability sampling, such as stratified or cluster sampling, which involve additional steps or criteria.

Explanations: In this scenario, the method of selecting three students by putting all the students' names in a hat and picking out three names randomly ensures that each student has an equal chance of being selected. This aligns with the definition of simple random sampling.

Option Analysis:

Option A: Correct. This method ensures each student has an equal chance of being selected, fitting the definition of simple random sampling.
Option B: Incorrect. Stratified random sampling involves dividing the population into subgroups and then randomly selecting from each subgroup, which is not described in the scenario.
Option C: Incorrect. Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters, which is not described in the scenario.
Option D: Incorrect. Systematic sampling involves selecting every nth member of the population after a random start, which is not described in the scenario.

8. What kind of sample technique is the following:Survey every 8th customer who leaves your store.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a population after a random start. In this case, every 8th customer is surveyed, which fits the definition of systematic sampling.

Common Mistakes: A common mistake is confusing systematic sampling with convenience sampling, where the sample is chosen based on ease of access rather than a fixed interval.

Explanations: Systematic sampling is a probability sampling method where every kth element is selected from a population after a random start. In this scenario, every 8th customer is surveyed, which means a fixed interval (k=8) is used to select the sample. This method ensures a more structured and representative sample compared to convenience sampling, which relies on ease of access.

Option Analysis:

Option A: Convenience Sampling is not correct because it involves selecting samples based on ease of access, not a fixed interval.
Option B: Simple Random Sampling is not correct because it involves selecting samples randomly without any fixed interval or pattern.
Option C: Systematic Sampling is correct because it involves selecting every kth element from a population after a random start, which matches the scenario described.
Option D: Sample is too general and does not specify the type of sampling method used.

9. An economist is studying the effect of education on salary and conducts a survey of 150 randomly selected workers from each of these categories:less than a high-school diploma, high-school diploma, more than a high-school diploma.

Correct Answer: Correct answer is: (D) Stratified random sampling.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

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

Common Mistakes: A common misunderstanding is confusing stratified random sampling with simple random sampling, where the entire population is treated as a single group and samples are selected randomly without any subgroup division.

Explanations: The economist divides the workers into three distinct categories based on their education level: less than a high-school diploma, high-school diploma, and more than a high-school diploma. Each category represents a stratum. By randomly selecting 150 workers from each stratum, the economist ensures that each education level is adequately represented in the sample. This method is characteristic of stratified random sampling.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This is not the case here, as the economist is not selecting entire clusters but rather individuals from each stratum.
Option B: Convenience sampling involves selecting individuals based on their availability and ease of access. The economist is not using convenience sampling, as the selection is random within each stratum.
Option C: Simple random sampling involves selecting individuals randomly from the entire population without any subgroup division. The economist is dividing the population into strata, which is not characteristic of simple random sampling.
Option D: Stratified random sampling involves dividing the population into strata and then randomly selecting individuals from each stratum. This matches the method used by the economist.
Option E: Systematic sampling involves selecting individuals at regular intervals from a list. The economist is not using a systematic approach but rather a stratified approach.

10. It is a process of selecting n sample size in the population via random number or through lottery method.

Correct Answer: Correct answer is: (A) Simple Random Sampling.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Simple Random Sampling is a method where each member of the population has an equal chance of being selected. This is typically done using random number generation or a lottery method.

Common Mistakes: A common misunderstanding is that other sampling methods like stratified, systematic, or cluster sampling also use random number generation or lottery methods. However, these methods involve additional steps beyond simple random selection.

Explanations: Simple Random Sampling involves selecting a sample size \( n \) from the population where each individual has an equal probability of being chosen. This can be achieved through random number generation or a lottery method, ensuring that the selection is unbiased and representative of the population.

Option Analysis:

Option A: Correct. Simple Random Sampling involves selecting a sample size \( n \) via random number generation or lottery method.
Option B: Incorrect. Stratified Random Sampling involves dividing the population into strata and then randomly selecting samples from each stratum.
Option C: Incorrect. Systematic Random Sampling involves selecting every \( k \)-th member of the population after a random start.
Option D: Incorrect. Cluster Random Sampling involves dividing the population into clusters and randomly selecting entire clusters.

Frequently Asked Questions

What is probability sampling?

Probability sampling is a method of selecting a sample from a population where each member has a known, non-zero chance of being selected. This ensures that the sample is representative of the population.

How does simple random sampling work?

Simple random sampling involves selecting a sample from a population in such a way that every member has an equal chance of being chosen. This can be done using methods like the lottery method or random number generation.

What is the purpose of stratified random sampling?

Stratified random sampling is used to ensure that specific subgroups within a population are adequately represented in the sample. The population is divided into strata, and random samples are taken from each stratum.

How is systematic sampling different from simple random sampling?

Systematic sampling involves selecting every nth member from a list after a random start, whereas simple random sampling selects members entirely at random. Systematic sampling can be easier to implement but may introduce bias if there is a pattern in the list.

Why is random selection important in probability sampling?

Random selection is crucial because it ensures that each member of the population has an equal chance of being included in the sample, which helps to minimize bias and improve the reliability of the results.

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