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Probability Sampling Quiz 13 (10 MCQs)

This set of multiple-choice questions evaluates understanding of probability sampling, including random selection, stratification, and proportional representation. Concepts covered include simple random sampling, stratified sampling, and systematic selection, ensuring an unbiased and representative sample. The questions assess the ability to apply these methods to ensure equal chance and proportional allocation within subgroups.

Quiz Instructions

Select an option to see the correct answer instantly.

1. This sample is selected by dividing the population into subgroups and then taking a fixed number of units from each group using the simple random sample.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) and then taking a simple random sample from each subgroup.

Common Mistakes: A common misunderstanding is confusing stratified sampling with cluster sampling, where the entire cluster is selected rather than a sample from each cluster.

Explanations: In stratified sampling, the population is divided into homogeneous subgroups (strata) based on certain characteristics. A simple random sample is then taken from each stratum. This ensures that each subgroup is represented in the sample, which can lead to more accurate and reliable results. The described method of dividing the population into subgroups and taking a fixed number of units from each group using simple random sampling aligns with the definition of stratified sampling.

Option Analysis:

Option A: Correct. Stratified sampling involves dividing the population into subgroups and taking a simple random sample from each subgroup.
Option B: Incorrect. Cluster sampling involves dividing the population into clusters and selecting entire clusters, not taking a sample from each cluster.
Option C: Incorrect. Judgment sampling is a non-probability sampling method where the researcher selects the sample based on their judgment, not a random process.
Option D: Incorrect. Experimental sampling is not a standard sampling method; it typically refers to the design of experiments rather than sampling techniques.

Mnemonic: S-S-S: Stratify, Sample, Stratified

2. Which statement best defines probability sampling in business research?

Correct Answer: Correct answer is: (B) Every population element has known nonzero selection chance.

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

Difficulty: Moderate

Concept notes: Probability sampling is a method where each member of the population has a known, nonzero chance of being selected. This ensures that the sample is representative of the population.

Common Mistakes: A common misunderstanding is that probability sampling involves selecting participants based on convenience or expert judgment, which is not accurate.

Explanations: In probability sampling, every element in the population has a known, nonzero probability of being selected. This ensures that the sample is representative of the population, reducing bias and increasing the reliability of the research findings.

Option Analysis:

Option A: This describes convenience sampling, not probability sampling.
Option B: This correctly defines probability sampling, where each population element has a known, nonzero chance of being selected.
Option C: This describes purposive or judgmental sampling, not probability sampling.
Option D: This describes voluntary response sampling, not probability sampling.

3. Every possible group of units of the required size has the same chance of being the selected sample as any other sample of the same size.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Simple random sampling is a method of selecting a sample from a population where every possible sample of a given size has an equal chance of being selected.

Common Mistakes: A common misunderstanding is that other sampling methods, such as stratified or cluster sampling, also ensure that every possible sample has the same chance of being selected. However, these methods introduce additional constraints that affect the probability of selection.

Explanations: In simple random sampling, each unit in the population has an equal probability of being selected, and every possible sample of the required size has the same chance of being the selected sample. This ensures that the sample is representative of the population and unbiased.

Option Analysis:

Option A: Simple Random sampling fits the description given in the question.
Option B: Thoughtful sampling is not a recognized probability sampling method.
Option C: Typical sampling is not a recognized probability sampling method.
Option D: Proportional sampling, such as stratified sampling, does not ensure that every possible sample has the same chance of being selected.

4. A researcher divides 300 students into two strata: 180 TVL and 120 GAS. Compute the sample from each stratum if total sample n = 150.

Correct Answer: Correct answer is: (A) Sample from TVL = (180/300) * 150 = 90; Sample from GAS = (120/300) * 150 = 60.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: In probability sampling, especially in stratified sampling, the sample size from each stratum is proportional to the size of the stratum in the population. This ensures that each stratum is adequately represented in the sample.

Common Mistakes: A common mistake is to misinterpret the proportion or to miscalculate the sample size for each stratum.

Explanations: To determine the sample size from each stratum, we use the formula: \[ \text{Sample size from stratum} = \left( \frac{\text{Size of stratum}}{\text{Total population}} \right) \times \text{Total sample size} \] For TVL: \[ \text{Sample size from TVL} = \left( \frac{180}{300} \right) \times 150 = 0.6 \times 150 = 90 \] For GAS: \[ \text{Sample size from GAS} = \left( \frac{120}{300} \right) \times 150 = 0.4 \times 150 = 60 \] Thus, the sample from TVL is 90 and the sample from GAS is 60.

Option Analysis:

Option A: Correct. The sample from TVL is 90 and the sample from GAS is 60.
Option B: Incorrect. The sample from TVL is 90, not 80, and the sample from GAS is 60, not 70.
Option C: Incorrect. The sample from TVL is 90, not 100, and the sample from GAS is 60, not 50.
Option D: Incorrect. The sample from TVL is 90, not 60, and the sample from GAS is 60, not 90.

5. Mrs. Combs samples her class by selecting 5 girls and 7 boys. This type of sampling is called?

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Stratified sampling involves dividing the population into distinct subgroups (strata) and then sampling from each subgroup. In this case, the population is divided into girls and boys, and samples are taken from each subgroup.

Common Mistakes: A common misunderstanding is to confuse stratified sampling with simple random sampling, where the entire population is treated as a single group and samples are taken randomly without regard to subgroups.

Explanations: Stratified sampling is the correct method because the population is divided into two distinct subgroups (girls and boys), and samples are taken from each subgroup. This ensures that both subgroups are represented in the sample, which is a key characteristic of stratified sampling.

Option Analysis:

Option A: Correct. Stratified sampling involves dividing the population into subgroups and sampling from each subgroup.
Option B: Incorrect. Systematic sampling involves selecting every kth element from a list after a random start, which is not the case here.
Option C: Incorrect. Simple random sampling involves selecting individuals randomly from the entire population without dividing into subgroups.
Option D: Incorrect. Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters, which is not the case here.

6. There is a rule applied to choose the sample. Put a Population in some order and select every "kth" Member

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every "kth" member from a population after it has been ordered in some way.

Common Mistakes: A common misunderstanding is confusing systematic sampling with simple random sampling, where each member of the population has an equal chance of being selected without any specific order.

Explanations: In systematic sampling, the population is first ordered in a specific sequence. Then, a starting point is chosen randomly, and every "kth" member is selected from this point onwards. This method ensures a spread of samples across the entire population, which can be more efficient and easier to implement than simple random sampling.

Option Analysis:

Option A: Convenience sampling involves selecting individuals based on ease of access, not a specific order or interval.
Option B: Simple random sampling involves selecting individuals randomly, where each member has an equal chance of being chosen, without any specific order or interval.
Option C: Systematic sampling involves selecting every "kth" member from an ordered population, which matches the description given in the question.
Option D: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each subgroup, not selecting every "kth" member.
Option E: Quota sampling involves selecting individuals to meet certain quotas, not based on a specific order or interval.

7. Mr. Snell assigns numbers 1-20 to all his students. He samples his class by picking 5 numbers randomly from his hat. 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 possible sample of a given size has an equal chance of being selected.

Common Mistakes: A common misunderstanding is confusing simple random sampling with other types of sampling methods, such as systematic or stratified sampling.

Explanations: In this scenario, Mr. Snell assigns numbers 1-20 to all his students and then picks 5 numbers randomly from his hat. 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 sampling involves selecting every kth element from a list after a random start. This is not the case here.
Option B: Simple random sampling involves selecting a sample where each member of the population has an equal chance of being chosen. This matches the scenario described.
Option C: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. This is not described in the scenario.
Option D: Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This is not described in the scenario.

8. A sample chosen at random form a randomly chosen subgroup or subgroups.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In stratified sampling, the population is divided into distinct subgroups (strata) based on certain characteristics. A random sample is then taken from each stratum. This ensures that each subgroup is represented in the sample.

Common Mistakes: A common misunderstanding is that a random sample (Option A) is the same as a stratified sample. However, a random sample does not necessarily ensure representation from all subgroups, whereas a stratified sample does.

Explanations: In stratified sampling, the population is first divided into distinct subgroups (strata) based on specific characteristics. A random sample is then taken from each stratum. This method ensures that each subgroup is adequately represented in the final sample. The description in the question matches this definition, as it mentions a sample chosen at random from a randomly chosen subgroup or subgroups.

Option Analysis:

Option A: A random sample is a selection method where each member of the population has an equal chance of being chosen, but it does not ensure representation from all subgroups.
Option B: A systematic sample involves selecting every nth member from a list after a random start, which does not necessarily involve dividing the population into subgroups.
Option C: A stratified sample involves dividing the population into subgroups and then randomly selecting from each subgroup, which matches the description in the question.
Option D: This option is incorrect as the correct answer is a stratified sample.

9. A sample is selected to match the distribution of age and religion that occurs in the population. This type of sample is called a

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: A stratified sample is a probability sampling method where the population is divided into subgroups (strata) based on specific characteristics, such as age and religion, and then samples are selected from each subgroup to ensure representation.

Common Mistakes: A common misunderstanding is confusing stratified sampling with matched sampling, where pairs of subjects are matched on specific characteristics, rather than ensuring proportional representation across strata.

Explanations: In stratified sampling, the population is divided into distinct subgroups (strata) based on characteristics like age and religion. A sample is then selected from each stratum to ensure that the sample reflects the population's distribution. This method ensures that the sample is representative of the population in terms of the specified characteristics.

Option Analysis:

Option A: A matched sample involves pairing subjects based on specific characteristics, not dividing the population into strata.
Option B: A stratified sample divides the population into strata and ensures proportional representation from each stratum.
Option C: A random sample does not ensure that specific characteristics are proportionally represented in the sample.
Option D: A convenience sample is selected based on ease of access, not on ensuring representation of specific characteristics.

10. Which of the following involves group-by-group selection of samples?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

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

Common Mistakes: A common misunderstanding is that simple random sampling also involves grouping, but it does not. Simple random sampling selects individuals from the entire population without any grouping.

Explanations: Stratified sampling involves dividing the population into distinct subgroups (strata) based on certain characteristics, such as age, gender, or income. After the population is divided into strata, samples are selected from each stratum. This ensures that each subgroup is represented in the sample, which can lead to more accurate and representative results.

Option Analysis:

Option A: Simple random sampling does not involve grouping the population into subgroups. It selects individuals randomly from the entire population.
Option B: Stratified sampling involves dividing the population into subgroups (strata) and then selecting samples from each subgroup.
Option C: Snowball sampling is a non-probability sampling technique where existing study subjects recruit future subjects from among their acquaintances. It does not involve group-by-group selection.
Option D: Quota sampling involves selecting individuals based on predefined quotas, but it does not necessarily involve group-by-group selection in the same way as stratified sampling.

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 and unbiased sample.

How does stratified sampling differ from simple random sampling?

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

What is the purpose of systematic sampling?

Systematic sampling involves selecting every kth member from an ordered population, providing a structured and efficient way to achieve a representative sample.

How is sample size determined in probability sampling?

Sample size in probability sampling is calculated based on the desired level of precision, confidence level, and variability within the population to ensure reliable results.

What is proportional allocation in stratified sampling?

Proportional allocation in stratified sampling means that the sample size from each stratum is proportional to the stratum's size in the population, ensuring that each subgroup is adequately represented.

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