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Probability Sampling Quiz 7 (10 MCQs)

This set of multiple-choice questions evaluates understanding of random selection, equal probability, and various sampling techniques, including simple random sampling, stratified sampling, and unbiased selection. It assesses the ability to apply these concepts to ensure representative and unbiased population division and randomization.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Each group of size "n" has an equal chance of being selected

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In simple random sampling, each group of size "n" has an equal chance of being selected. This ensures that every possible sample of a given size has an equal probability of being chosen.

Common Mistakes: A common misunderstanding is that other sampling methods, such as convenience or quota sampling, also ensure equal chances of selection. However, these methods do not provide the same level of randomness and equal probability.

Explanations: Simple random sampling is the method where each group of size "n" has an equal chance of being selected. This ensures that the sample is representative of the population and that no bias is introduced in the selection process. Other methods like convenience or quota sampling do not guarantee equal chances for all groups.

Option Analysis:

Option A: Convenience sampling involves selecting individuals that are easiest to reach, which does not ensure equal chances for all groups.
Option B: Simple random sampling ensures that each group of size "n" has an equal chance of being selected, making it the correct answer.
Option C: Systematic sampling involves selecting every kth element from a list, which does not ensure equal chances for all groups.
Option D: Stratified sampling involves dividing the population into strata and then sampling from each stratum, which does not ensure equal chances for all groups of size "n".
Option E: Quota sampling involves selecting individuals to meet certain quotas, which does not ensure equal chances for all groups.

2. Random sampling does not

Correct Answer: Correct answer is: (D) Maximize experimental variance.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Random sampling is a probability sampling technique that aims to ensure each member of the population has an equal chance of being selected. This method is used to make the sample representative of the population, reduce error, and increase the precision of the experiment.

Common Mistakes: A common misunderstanding is that random sampling increases experimental variance. In fact, random sampling aims to minimize variance and ensure that the sample accurately reflects the population.

Explanations: Random sampling does not maximize experimental variance. Instead, it aims to minimize variance by ensuring that each member of the population has an equal chance of being selected. This helps to make the sample representative of the population, which in turn reduces error and increases the precision of the experiment.

Option Analysis:

Option A: Random sampling does make the sample representative of the population by ensuring each member has an equal chance of being selected.
Option B: Random sampling does ensure generalization of results by making the sample representative of the population.
Option C: Random sampling does reduce error and increase precision of the experiment by minimizing variance.
Option D: Random sampling does not maximize experimental variance; it aims to minimize it.

3. When each member of a population has an equal chance of being selected, this is called:

Correct Answer: Correct answer is: (C) A random probability sample.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: In probability sampling, each member of 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, such as stratified sampling, also ensure equal chances for each member. However, stratified sampling involves dividing the population into subgroups and then sampling from each subgroup, which does not necessarily mean each member has an equal chance of being selected.

Explanations: A random probability sample is the correct answer because it ensures that each member of the population has an equal chance of being selected. This method is fundamental in probability sampling, as it minimizes bias and ensures that the sample accurately reflects the population.

Option Analysis:

Option A: A snowball sample is a non-probability sampling method where existing study subjects recruit future subjects from among their acquaintances. This does not ensure equal chances for each member of the population.
Option B: A stratified sample involves dividing the population into subgroups (strata) and then sampling from each subgroup. While it can be a probability sampling method, it does not inherently ensure that each member has an equal chance of being selected.
Option C: A random probability sample ensures that each member of the population has an equal chance of being selected, which is the definition of probability sampling.
Option D: A non-random sample does not ensure that each member of the population has an equal chance of being selected, as it often involves convenience or judgmental selection methods.

4. A simple random sample is one in which:

Correct Answer: Correct answer is: (D) Every unit of the population has an equal chance of being selected.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A simple random sample is a type of probability sampling where each member of the population has an equal chance of being selected.

Common Mistakes: A common misunderstanding is that simple random sampling involves selecting every nth unit from a list, which is actually systematic sampling.

Explanations: In simple random sampling, each unit in the population has an equal probability of being chosen. This ensures that the sample is representative of the population and reduces bias. The key feature is the equal chance of selection for each unit.

Option Analysis:

Option A: This describes systematic sampling, not simple random sampling.
Option B: This describes non-probability sampling, which is not the same as simple random sampling.
Option C: This describes quota sampling, which is a type of non-probability sampling.
Option D: This correctly describes simple random sampling, where each unit has an equal chance of being selected.

5. What kind of sample technique is the following:Select at random 150 parents of high school and send them a survey.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

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 that any random selection is simple random sampling. However, simple random sampling specifically requires that each member of the population has an equal chance of being selected.

Explanations: The technique described involves selecting 150 parents at random and sending them a survey. This method ensures that each parent has an equal chance of being selected, which aligns with the definition of Simple Random Sampling.

Option Analysis:

Option A: Convenience Sampling involves selecting individuals who are easiest to reach, which does not ensure equal probability of selection.
Option B: Simple Random Sampling ensures each member of the population has an equal chance of being selected, which matches the described method.
Option C: Systematic Sampling involves selecting every nth member from a list, which does not match the described random selection.
Option D: "Sample" is too general and does not specify the sampling technique.

6. What is a key assumption of simple random sampling?

Correct Answer: Correct answer is: (D) Equal and likely chance for every item.

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 each member of the population has an equal and independent chance of being selected.

Common Mistakes: A common misunderstanding is that simple random sampling involves some form of judgment or sorting, which is not the case. Each item must have an equal chance of being selected.

Explanations: In simple random sampling, every item in the population has an equal and likely chance of being selected. This ensures that the sample is representative of the population and reduces bias. The other options describe methods that do not align with the principles of simple random sampling.

Option Analysis:

Option A: This option suggests sorting items in reverse order, which is not a characteristic of simple random sampling. Sorting introduces a systematic bias.
Option B: This option implies that the selection is based on researcher judgment, which contradicts the principle of randomness in simple random sampling.
Option C: This option suggests that the interval changes with each selection, which is not a feature of simple random sampling. This would be more characteristic of systematic sampling.
Option D: This option correctly states that every item has an equal and likely chance of being selected, which is a key assumption of simple random sampling.

7. In ..... every member of the target population has an equal chance of becoming part of the sample.

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

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

Difficulty: Easy

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

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

Explanations: In random sampling, each member of the population has an equal and independent chance of being selected. This ensures that the sample is representative of the entire population, as no individual is favored or excluded based on any characteristic.

Option Analysis:

Option A: Stratified sampling involves dividing the population into subgroups (strata) and then randomly selecting from each stratum. This does not ensure that every member has an equal chance of being selected overall.
Option B: Random sampling ensures that every member of the population has an equal chance of being selected, making it the correct answer.
Option C: Opportunity sampling involves selecting individuals who are conveniently available, which does not ensure equal probability for every member of the population.
Option D: Self-selected sampling involves individuals volunteering to be part of the sample, which also does not ensure equal probability for every member of the population.

8. A teacher chooses her "student of the week" by choosing a name out of a hat. What is this an example of?

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.

Common Mistakes: A common misunderstanding is that other sampling methods, such as systematic or convenience sampling, might also apply. However, these methods do not ensure that each individual has an equal chance of being chosen.

Explanations: In this scenario, the teacher is choosing a name out of a hat, which means every student has an equal chance of being selected. This aligns with the definition of Simple Random Sampling, where each member of the population has an equal and independent chance of being chosen.

Option Analysis:

Option A: Correct. Simple Random Sampling ensures each student has an equal chance of being selected.
Option B: Incorrect. Systematic Sampling involves selecting every nth member from a list, which is not the case here.
Option C: Incorrect. Convenience Sampling involves selecting individuals based on ease of access, which is not the case here.
Option D: Incorrect. Quota Sampling involves selecting individuals to meet specific quotas, which is not the case here.
Option E: Incorrect. Stratified Sampling involves dividing the population into strata and then sampling from each stratum, which is not the case here.

9. What is the main characteristic of Stratified Sampling?

Correct Answer: Correct answer is: (A) It involves dividing the population into subgroups.

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, or strata, based on specific characteristics. Samples are then drawn from each stratum to ensure representation from all segments of the population.

Common Mistakes: A common misunderstanding is that stratified sampling involves random selection without any grouping. However, the key feature is the division of the population into subgroups before sampling.

Explanations: Stratified sampling involves dividing the population into subgroups based on specific characteristics, such as age, gender, or income. This ensures that each subgroup is adequately represented in the sample, leading to more accurate and reliable results. The other options do not accurately describe the main characteristic of stratified sampling.

Option Analysis:

Option A: Correct. Stratified sampling involves dividing the population into subgroups based on specific characteristics.
Option B: Incorrect. Stratified sampling involves grouping before random selection, not random selection without grouping.
Option C: Incorrect. Stratified sampling considers multiple characteristics to form subgroups, not just a single characteristic.
Option D: Incorrect. Stratified sampling does not require a fixed sample size for all subgroups; the sample size can vary based on the stratum size.

10. This Sampling technique uses randomization to make sure that every element of the population gets an equal chance to be part of the selected sample.

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Easy

Concept notes: Probability sampling is a technique where each member of the population has an equal chance of being selected for the sample. This ensures that the sample is representative of the entire population.

Common Mistakes: A common misunderstanding is that non-probability sampling also ensures equal chances for each element, but it does not use randomization to ensure this.

Explanations: Probability sampling uses randomization to ensure that every element of the population has an equal chance of being included in the sample. This method is designed to minimize bias and ensure that the sample accurately reflects the population.

Option Analysis:

Option A: Probability Sampling is the correct choice because it uses randomization to ensure that every element of the population has an equal chance of being selected.
Option B: Non-Probability Sampling does not use randomization to ensure equal chances for each element, making it less representative of the population.

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 unbiased selection.

How does simple random sampling work?

Simple random sampling involves selecting individuals from a population completely at random, ensuring each member has an equal probability of being included in the sample.

What is the main advantage of using probability sampling?

The main advantage of probability sampling is that it minimizes bias and allows for the estimation of experimental variance, leading to more reliable results.

Can you explain stratified sampling?

Stratified sampling involves dividing the population into subgroups (strata) based on certain characteristics and then randomly selecting samples from each subgroup.

Why is randomization important in probability sampling?

Randomization is crucial because it ensures that each member of the population has an equal chance of being selected, which helps to reduce bias and improve the representativeness of the sample.

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