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Probability Sampling Quiz 16 (10 MCQs)

This set of multiple-choice questions evaluates understanding of probability sampling methods, including simple random sampling, stratified sampling, and proportional representation. It assesses the ability to apply concepts of equal probability, independent selection, and random sampling within strata to ensure a representative sample. The questions cover dividing populations into subgroups, random selection processes, and unbiased sampling techniques.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Probability sampling means?

Correct Answer: Correct answer is: (A) Every individual has chance of being selected.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Probability sampling is a method of selecting a sample from a population where each individual has a known, non-zero probability of being selected.

Common Mistakes: A common misunderstanding is that probability sampling means every individual has an equal chance of being selected, which is not always the case. The key is that each individual has a known, non-zero probability.

Explanations: In probability sampling, each individual in the population has a chance of being selected, which ensures that the sample is representative of the population. This method allows for statistical inference about the population based on the sample data.

Option Analysis:

Option A: Correct. This option accurately describes the core principle of probability sampling.
Option B: Incorrect. This option contradicts the definition of probability sampling, as it implies no probability is associated with selection.
Option C: Incorrect. This option is not applicable as one of the other options is correct.
Option D: Incorrect. This option is not applicable as one of the other options is correct.

2. Dividing a population into subgroups and sampling proportionally from each is:

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing a population into distinct subgroups (strata) and then sampling proportionally from each subgroup.

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 (stratum) is represented in the sample in proportion to its size in the population. This method is particularly useful when the population has distinct subgroups that may differ significantly from each other. By sampling proportionally from each stratum, the sample is more representative of the entire population.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters. This is different from stratified sampling, where each stratum is sampled proportionally.
Option B: Quota sampling involves selecting a sample to match the proportions of certain characteristics in the population, but it is not a probability sampling method and does not ensure random selection within each subgroup.
Option C: Stratified sampling involves dividing the population into subgroups (strata) and sampling proportionally from each stratum, which matches the description given in the question.
Option D: Systematic sampling involves selecting every kth element from a list after a random start. This method does not involve dividing the population into subgroups and sampling proportionally from each.

Mnemonic: S-P-S: Stratified, Proportional, Subgroups

3. What kind of sample technique is the following:Survey 130 names chosen out of a hat.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Simple 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 Simple Random Sampling with Convenience Sampling, where participants are chosen based on ease of access rather than random selection.

Explanations: In this scenario, surveying 130 names chosen out of a hat ensures that each name has an equal chance of being selected, which aligns with the definition of Simple Random Sampling. This method does not involve any systematic or convenience-based selection, making it a clear example of Simple Random Sampling.

Option Analysis:

Option A: Convenience Sampling involves selecting participants based on ease of access, which is not the case here.
Option B: Simple Random Sampling is the correct choice as each name has an equal chance of being selected.
Option C: Systematic Sampling involves selecting every nth member from a list, which is not the method used here.
Option D: "Sample" is too general and does not specify the type of sampling technique used.

4. Ms. Noelle draws a sample on her class by picking 10 numbers from her hat and each number is assigned to a student. This is ..... sampling.

Correct Answer: Correct answer is: (B) Simple Random.

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

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. This is typically done by using a random method, such as drawing numbers from a hat.

Common Mistakes: A common misunderstanding is confusing simple random sampling with other types of sampling methods, such as systematic random sampling, stratified sampling, or cluster sampling. Each of these methods has distinct characteristics and procedures.

Explanations: In this scenario, Ms. Noelle is using a method where she draws 10 numbers from a hat, and each number is assigned to a student. This method ensures that each student has an equal chance of being selected, which aligns with the definition of simple random sampling.

Option Analysis:

Option A: Systematic Random sampling involves selecting every kth element from a list after a random start. This is not the case here as the numbers are drawn randomly without a systematic pattern.
Option B: Simple Random sampling involves each member of the population having an equal chance of being selected, which matches the method described in the question.
Option C: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. This is not described in the question.
Option D: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This is not described in the question.

5. Which sampling method gives every item/person in the population an equal chance of being selected?

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

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

Difficulty: Easy

Concept notes: In probability sampling, every item or person in the population has an equal chance of being selected. This ensures that the sample is representative of the entire population.

Common Mistakes: A common misunderstanding is that other sampling methods like judgement sampling or quota sampling also provide an equal chance of selection, but they do not. These methods rely on subjective criteria or predefined quotas, which can introduce bias.

Explanations: Random sampling is the only method among the options that ensures every item or person in the population has an equal chance of being selected. This is because random sampling uses a random selection process, such as drawing names from a hat or using a random number generator, to ensure that each member of the population has an equal probability of being included in the sample.

Option Analysis:

Option A: Judgement Sampling involves selecting items based on the researcher's judgement, which does not provide an equal chance of selection for all items in the population.
Option B: Quota Sampling involves selecting items to meet certain quotas, which also does not provide an equal chance of selection for all items in the population.
Option C: Random Sample ensures that every item or person in the population has an equal chance of being selected, making it the correct answer.
Option D: Opportunity Sampling involves selecting items based on convenience or availability, which does not provide an equal chance of selection for all items in the population.

6. Farmer Jose separates his farm into 10 regions. He then randomly selected a proportional number of tress from each region to estimate the number of apples produced on his apple tree farm. This is ..... sampling.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

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

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: Farmer Jose divides his farm into 10 regions, which are the strata. He then randomly selects a proportional number of trees from each region. This method ensures that each region (stratum) is represented in the sample, which is the essence of stratified sampling.

Option Analysis:

Option A: Cluster sampling involves selecting entire clusters (regions) rather than sampling from within each cluster. This does not apply here as Farmer Jose is sampling from within each region.
Option B: Systematic random sampling involves selecting every nth item from a list after a random start. This does not apply here as the sampling is not based on a systematic selection from a list.
Option C: Stratified sampling involves dividing the population into strata and then sampling from each stratum. This matches the scenario where Farmer Jose divides his farm into regions and samples from each region.
Option D: Simple random sampling involves selecting items entirely at random from the entire population without any stratification. This does not apply here as the sampling is done within predefined regions.

Mnemonic: Stratified: "Strata" for "Stratified" - think of layers in a cake.

7. Is a sample selected from a population in such a way that every member of the population has an equal chance of being selected & the selection of any individual does not influence the selection of any other.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. The selection of any individual does not influence the selection of any other.

Common Mistakes: A common misunderstanding is that other sampling methods, such as stratified sampling, also ensure equal probability of selection for each member. However, stratified sampling involves dividing the population into subgroups and then sampling from each subgroup, which does not necessarily ensure equal probability for each individual.

Explanations: A simple random sample ensures that every member of the population has an equal chance of being selected, and the selection of one individual does not affect the selection of another. This aligns with the definition provided in the question.

Option Analysis:

Option A: Stratified sample involves dividing the population into subgroups and then sampling from each subgroup, which does not ensure equal probability for each individual.
Option B: Non-random sample does not ensure that every member of the population has an equal chance of being selected.
Option C: Simple random sample ensures that every member of the population has an equal chance of being selected, and the selection of one individual does not affect the selection of another.
Option D: Complex random sample involves more complicated sampling techniques that may not ensure equal probability for each individual.

8. The student population at the local middle school is divided into groups using birth month (12 groups). Ten students from each birth month group are randomly selected to participate in an afterschool program.

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

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

Difficulty: Moderate

Explanations: The student population is divided into 12 groups based on birth month, which are the strata. Then, 10 students are randomly selected from each stratum. This method ensures that each birth month group is represented in the sample, which is the essence of stratified sampling.

Option Analysis:

Option A: Random sampling involves selecting individuals from the entire population without any specific grouping. This does not apply here as the population is divided into groups first.
Option B: Systematic sampling involves selecting every nth individual from a list. This does not apply here as the population is divided into groups and then sampled.
Option C: Convenience sampling involves selecting individuals based on ease of access. This does not apply here as the selection is random within each group.
Option D: Stratified sampling involves dividing the population into strata and then randomly selecting samples from each stratum. This matches the described method.
Option E: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This does not apply here as individual students are selected from each group.

Mnemonic: Stratified: "Strata" for "Stratified" - think of layers in a cake, each layer is sampled.

9. When it comes to representativeness in standardised sampling, which one of the following is less likely to select a biased sample?

Correct Answer: Correct answer is: (B) 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 stratum. This method ensures that each subgroup is represented in the sample, reducing the likelihood of bias.

Common Mistakes: A common misunderstanding is that simple random sampling is always the best method for representativeness. However, stratified random sampling can be more effective in ensuring that all subgroups are adequately represented.

Explanations: Stratified random sampling is less likely to select a biased sample because it ensures that each subgroup within the population is represented proportionally. By dividing the population into strata and then randomly selecting samples from each stratum, the method reduces the risk of underrepresentation or overrepresentation of any particular subgroup.

Option Analysis:

Option A: Simple random sampling involves selecting individuals from the population entirely by chance, which can sometimes lead to underrepresentation or overrepresentation of certain subgroups, potentially introducing bias.
Option B: Stratified random sampling involves dividing the population into strata and then randomly selecting samples from each stratum, ensuring that each subgroup is represented proportionally, reducing the likelihood of bias.
Option C: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This method can introduce bias if the clusters are not representative of the population as a whole.
Option D: Snowball sampling relies on referrals from initial subjects to generate additional subjects. This method is prone to bias as it may not represent the entire population and can lead to a non-representative sample.

10. A researcher divides a population into subgroups and randomly selects participants from each subgroup. This is called:

Correct Answer: Correct answer is: (A) Stratified Sampling.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

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

Common Mistakes: A common misunderstanding is confusing stratified sampling with other sampling methods, such as convenience sampling, which involves selecting participants based on ease of access rather than random selection from subgroups.

Explanations: Stratified sampling is the correct answer because it involves dividing the population into subgroups (strata) and then randomly selecting participants from each subgroup. This method ensures that each subgroup is adequately represented in the sample, which can lead to more accurate and reliable results.

Option Analysis:

Option A: Correct. Stratified sampling involves dividing the population into subgroups and randomly selecting participants from each subgroup.
Option B: Incorrect. Convenience sampling involves selecting participants based on ease of access, not random selection from subgroups.
Option C: Incorrect. Systematic sampling involves selecting every nth member of the population, not dividing into subgroups and randomly selecting from each.
Option D: Incorrect. Snowball sampling involves selecting participants through referrals from initial participants, not dividing into subgroups and randomly selecting from each.

Mnemonic: S-S-S: Stratify, Select, Sample

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 individuals from a population in such a way that each individual has an equal chance of being chosen. This can be done using random number generators or lottery methods.

What is the purpose of stratified random sampling?

Stratified random sampling is used to ensure that specific subgroups within a population are proportionally represented in the sample. This method involves dividing the population into strata and then randomly selecting individuals from each stratum.

Why is representativeness important in probability sampling?

Representativeness is crucial because it ensures that the sample accurately reflects the characteristics of the entire population. This allows for more reliable and valid inferences to be made about the population based on the sample data.

How does probability sampling differ from non-probability sampling?

Probability sampling involves random selection, where each member of the population has a known chance of being included in the sample. Non-probability sampling does not use random selection, and the likelihood of inclusion is unknown, which can lead to bias.

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