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Probability Sampling Quiz 17 (10 MCQs)

This set of multiple-choice questions evaluates understanding of stratified sampling, including population division into strata, random selection within strata, and ensuring representative samples. Concepts such as probability sampling, random sampling, and unbiased sampling methods are also covered.

Quiz Instructions

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1. Systematic sampling involves selecting every nth member of a population.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Systematic sampling is a probability sampling method where every nth member of a population is selected after a random start.

Common Mistakes: A common misunderstanding is that systematic sampling involves random selection of every nth member without a starting point, which is incorrect. The method requires a random start followed by a fixed interval.

Explanations: Systematic sampling involves selecting every nth member of a population after a random start. This method ensures that the sample is spread evenly throughout the population, providing a representative sample. The key steps are to determine the sampling interval (n) and then select every nth member starting from a randomly chosen point. This method is straightforward and efficient, making it a popular choice in probability sampling.

Option Analysis:

Option A: This option is correct because systematic sampling indeed involves selecting every nth member of a population after a random start.
Option B: This option is incorrect because it contradicts the definition and process of systematic sampling.

2. To estimate the total amount of unpaid balances of their customers, a convenience store selected using the lottery method 100 customers from their list of charge accounts.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Simple random sampling is a method where each member of the population has an equal chance of being selected. This is achieved by using a lottery method or random number generation.

Common Mistakes: A common misunderstanding is confusing simple random sampling with other sampling methods like stratified or cluster sampling, which involve additional steps or grouping.

Explanations: The convenience store selected 100 customers from their list of charge accounts using the lottery method. This method ensures that each customer has an equal chance of being selected, which aligns with the definition of simple random sampling. The lottery method is a straightforward way to achieve a random selection without any additional stratification or clustering.

Option Analysis:

Option A: Systematic sampling involves selecting every kth element from a list after a random start. This is not the case here as the selection was done using a lottery method.
Option B: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. The question does not mention any stratification.
Option C: Simple random sampling is the correct method as each customer has an equal chance of being selected through the lottery method.
Option D: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. The question does not mention any clustering.

3. In here the elements of the population are put into a list then every ith element in the list is chosen(systematically) for inclusion in the sample.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every ith element from a list after a random start.

Common Mistakes: A common misunderstanding is confusing systematic sampling with simple random sampling, where each element has an equal chance of being selected independently.

Explanations: In systematic sampling, the population is first listed, and then every ith element is chosen after a random start. This method ensures a systematic and evenly distributed sample across the population. The key feature is the fixed interval between selections, which is not present in other sampling methods like simple random sampling or stratified sampling.

Option Analysis:

Option A: Probability sampling is a broader category that includes systematic sampling, but it does not specify the systematic selection method.
Option B: Non-probability sampling does not involve a random selection process, which is contrary to the systematic selection described.
Option C: Simple random sampling involves selecting elements randomly without any fixed interval, unlike systematic sampling.
Option D: Systematic sampling involves selecting every ith element from a list after a random start, which matches the description given.
Option E: Stratified sampling involves dividing the population into strata and then sampling from each stratum, which is different from the systematic selection described.

4. Sampling technique where each member has equal chance:

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

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 that other sampling methods like stratified or purposive sampling also ensure equal chances for each member, which is not true.

Explanations: In random sampling, every individual in the population has an equal probability of being chosen, ensuring that the sample is representative of the entire population. This method eliminates bias and ensures that the sample accurately reflects the population characteristics.

Option Analysis:

Option A: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. This does not ensure that each member has an equal chance of being selected overall.
Option B: Purposive sampling involves selecting individuals based on specific criteria, which does not provide an equal chance for each member of the population.
Option C: Random sampling ensures that each member of the population has an equal chance of being selected, making it the correct answer.
Option D: Snowball sampling involves selecting participants through referrals from initial subjects, which does not ensure an equal chance for each member of the population.

5. When there is a need to apply different data collection methods to different parts of the population, the best sampling method would be

Correct Answer: Correct answer is: (C) 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 method is particularly useful when different parts of the population require different data collection methods.

Common Mistakes: A common misunderstanding is that cluster sampling or systematic sampling might be the best method for applying different data collection methods to different parts of the population. However, these methods do not inherently account for the need to apply different methods to different subgroups.

Explanations: Stratified random sampling is the best method when different parts of the population require different data collection methods. By dividing the population into strata, each stratum can be sampled using the most appropriate method for that subgroup, ensuring that the data collected is representative and accurate for each subgroup.

Option Analysis:

Option A: Double sampling is a method where a preliminary sample is taken to estimate the population parameters, and then a second sample is taken to refine the estimates. This method does not inherently address the need to apply different data collection methods to different parts of the population.
Option B: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters for sampling. This method is useful when the population is geographically dispersed, but it does not address the need to apply different data collection methods to different parts of the population.
Option C: Stratified random sampling involves dividing the population into distinct subgroups (strata) and then randomly selecting samples from each subgroup. This method is particularly useful when different parts of the population require different data collection methods, as each stratum can be sampled using the most appropriate method for that subgroup.
Option D: Systematic random sampling involves selecting every kth element from a list after a random start. This method does not inherently address the need to apply different data collection methods to different parts of the population.

6. Which of the following is the first step when using stratified sampling?

Correct Answer: Correct answer is: (A) Identifying the strata.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) based on specific characteristics before sampling.

Common Mistakes: A common mistake is to start with calculating proportions or randomly selecting participants without first identifying the strata.

Explanations: In stratified sampling, the first step is to identify the strata. This involves dividing the population into homogeneous subgroups based on a characteristic of interest. Once the strata are identified, the subsequent steps of calculating proportions and randomly selecting participants from each stratum can be carried out.

Option Analysis:

Option A: Correct. Identifying the strata is the first step in stratified sampling.
Option B: Incorrect. Calculating the proportions needed for the sample is a subsequent step after identifying the strata.
Option C: Incorrect. Randomly selecting the proportion needed for each stratum is done after identifying the strata and calculating the proportions.
Option D: Incorrect. Randomly allocating participants to each condition is not a step in stratified sampling.

7. Which sampling method divides population into strata?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Stratified sampling is a probability sampling method where the population is divided into distinct, non-overlapping subgroups called strata. Each stratum is homogeneous within itself but heterogeneous across strata. Samples are then drawn from each stratum.

Common Mistakes: A common misunderstanding is confusing stratified sampling with cluster sampling. In cluster sampling, the population is divided into clusters, and entire clusters are randomly selected, whereas in stratified sampling, samples are taken from each stratum.

Explanations: Stratified sampling divides the population into homogeneous subgroups (strata) based on specific characteristics. This ensures that each subgroup is adequately represented in the sample, leading to more precise estimates. The other methods do not involve dividing the population into strata.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters. It does not involve dividing the population into strata.
Option B: Stratified sampling involves dividing the population into strata and then sampling from each stratum. This is the correct method for dividing the population into homogeneous subgroups.
Option C: Systematic sampling involves selecting every kth element from a list after a random start. It does not involve dividing the population into strata.
Option D: Simple random sampling involves selecting individuals from the population entirely at random. It does not involve dividing the population into strata.

8. Which statement best defines stratified sampling?

Correct Answer: Correct answer is: (C) Dividing the population into strata, sampling within each stratum.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified sampling is a probability sampling technique where the population is divided into distinct subgroups (strata) based on specific characteristics, and then samples are taken from each stratum.

Common Mistakes: A common misunderstanding is confusing stratified sampling with cluster sampling, where the population is divided into clusters and entire clusters are randomly selected.

Explanations: Stratified sampling ensures that each subgroup within the population is represented in the sample. This method is particularly useful when the population has distinct subgroups that may differ significantly from each other. By dividing the population into strata and sampling within each stratum, the sample can more accurately reflect the diversity of the population.

Option Analysis:

Option A: This describes convenience sampling, not stratified sampling.
Option B: This describes simple random sampling, not stratified sampling.
Option C: This correctly describes stratified sampling, where the population is divided into strata and samples are taken from each stratum.
Option D: This describes cluster sampling, not stratified sampling.

9. Every person in the population has an equal chance of being selected-which sampling method

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

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

Common Mistakes: A common misunderstanding is that other sampling methods like systematic or quota sampling also ensure equal chances for every individual, but they do not.

Explanations: In random sampling, each member of the population has an equal probability of being chosen, ensuring that the sample is representative of the entire population. This method eliminates bias and ensures that every individual has an equal chance of being included in the sample.

Option Analysis:

Option A: Systematic sampling involves selecting every nth individual from a list, which does not guarantee equal chances for all individuals.
Option B: Quota sampling involves selecting individuals to meet specific quotas, which can introduce bias and does not ensure equal chances for all individuals.
Option C: Volunteer sampling relies on individuals who volunteer, which can introduce selection bias and does not ensure equal chances for all individuals.
Option D: Random sampling ensures that every individual in the population has an equal chance of being selected, making it the correct answer.

10. Name the sampling method:I break the classes (Freshman, sophomore, junior, and senior) into groups and then randomly sample 25 students from those groups.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) based on shared characteristics and then randomly sampling from each subgroup.

Common Mistakes: A common mistake is confusing stratified sampling with cluster sampling. In cluster sampling, the population is divided into clusters, and entire clusters are randomly selected, whereas in stratified sampling, samples are taken from each stratum.

Explanations: The method described involves breaking the classes (Freshman, sophomore, junior, and senior) into groups and then randomly sampling 25 students from each group. This matches the definition of stratified sampling, where the population is divided into strata and a random sample is taken from each stratum.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters. This does not match the described method.
Option B: Stratified sampling involves dividing the population into strata and randomly sampling from each stratum. This matches the described method.
Option C: Simple random sampling involves selecting individuals from the entire population without any grouping. This does not match the described method.
Option D: Group sampling is not a standard term in probability sampling. This does not match the described method.

Mnemonic: S-S-S: Stratify, Sample, Strata

Frequently Asked Questions

What is probability sampling?

Probability sampling is a method of selecting a sample from a population where each member has an equal chance of being chosen, ensuring a representative sample.

How does stratified random sampling differ from simple random sampling?

Stratified random sampling divides the population into subgroups (strata) based on shared characteristics, then randomly selects samples from each stratum, while simple random sampling selects individuals entirely at random without stratification.

What is the purpose of using systematic sampling?

Systematic sampling involves selecting every nth member from a list after a random start, which simplifies the sampling process while maintaining a representative sample.

How can the lottery method be used in probability sampling?

The lottery method involves assigning numbers to each member of the population and drawing numbers randomly, ensuring each member has an equal chance of being selected for the sample.

Why is it important to use probability sampling in research?

Probability sampling ensures that the sample is representative of the population, reducing bias and improving the reliability and validity of research findings.

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