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Probability Sampling Quiz 33 (5 MCQs)

This quiz evaluates understanding of stratified random sampling, random sampling within strata, and representation of subgroups. It covers probability sampling methods, systematic selection, fixed interval sampling, and cluster selection. The material assesses knowledge of population division, sampling methods, and selection bias.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Probability sampling ensures what key property for each member of the population?

Correct Answer: Correct answer is: (D) Known nonzero chance of selection.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: Probability sampling ensures that each member of the population has a known, nonzero chance of being selected for the sample.

Common Mistakes: A common misunderstanding is that probability sampling guarantees equal representation or equal measurement reliability, which is not necessarily true.

Explanations: Probability sampling is a method where each member of the population has a known, nonzero probability of being selected. This ensures that the sample is representative of the population and reduces selection bias. The key property is that the selection process is based on known probabilities, not convenience or other non-random criteria.

Option Analysis:

Option A: This option is incorrect because probability sampling does not ensure accurate description of measured variables; it only ensures a known chance of selection.
Option B: This option is incorrect because probability sampling does not ensure equal measurement reliability across groups; it only ensures a known chance of selection.
Option C: This option is incorrect because probability sampling is not based on convenience; it is based on known probabilities.
Option D: This option is correct because probability sampling ensures that each member of the population has a known, nonzero chance of being selected.

2. A researcher wants to study the relationship of family size to income. He classifies his population into different income slabs and then takes a random sample from each slab in order. Which technique of sampling is he working with?

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) based on a characteristic, and then taking a random sample from each subgroup.

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

Explanations: The researcher classifies the population into different income slabs, which are the strata. Then, he takes a random sample from each slab. This method ensures that each income slab is represented in the sample, which is the essence of stratified random sampling.

Option Analysis:

Option A: Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters. This is not the case here, as the researcher is taking samples from each income slab, not entire clusters.
Option B: Random sampling involves selecting individuals from the entire population without any specific grouping. This does not apply here as the population is divided into income slabs first.
Option C: Stratified random sampling involves dividing the population into strata and then taking a random sample from each stratum. This matches the researcher's method of dividing the population into income slabs and then sampling from each slab.
Option D: Systematic sampling involves selecting every nth individual from a list. This does not apply here as the researcher is dividing the population into income slabs and then sampling from each slab.

Mnemonic: SRS: Stratify, Randomly Sample

3. Choosing every 4th house on a street is an example of:

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

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

Difficulty: Moderate

Concept notes: Systematic sampling involves selecting every kth element from a list or sequence after a random start. In this case, choosing every 4th house is a clear example of systematic sampling.

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: Systematic sampling involves selecting every kth element from a list or sequence after a random start. In this scenario, choosing every 4th house on a street fits the definition of systematic sampling because it follows a fixed interval (every 4th house) after an initial random start.

Option Analysis:

Option A: Opportunity sampling involves selecting individuals who are conveniently available, which does not apply to the systematic selection of every 4th house.
Option B: Volunteer sampling involves individuals who volunteer to participate, which is not relevant to the systematic selection of houses.
Option C: Systematic sampling involves selecting every kth element from a list or sequence, which matches the scenario of choosing every 4th house.
Option D: Stratified sampling involves dividing the population into subgroups and then sampling from each subgroup, which does not apply to the systematic selection of every 4th house.

4. Members of the population are grouped; one or more groups are selected at random. All members of that group are included in the sample.

Correct Answer: Correct answer is: (A) Cluster sample.

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

Concept notes: In cluster sampling, the population is divided into groups (clusters), and entire clusters are randomly selected for the sample. This method is useful when the population is large and spread out geographically.

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

Explanations: Cluster sampling involves dividing the population into clusters and then randomly selecting one or more clusters. All members of the selected clusters are included in the sample. This method is efficient when the population is large and spread out, as it reduces the need to sample from every part of the population.

Option Analysis:

Option A: Correct. Cluster sampling involves selecting entire groups (clusters) at random and including all members of those clusters in the sample.
Option B: Incorrect. Simple random sampling involves selecting individuals from the entire population at random, not groups.
Option C: Incorrect. Stratified sampling involves dividing the population into strata and then sampling from each stratum, not selecting entire groups.
Option D: Incorrect. Proportional sampling is a type of stratified sampling where the sample size from each stratum is proportional to the stratum's size in the population.

5. Sampling technique which follows every n$^{th}$ element chosen start random and picking every n$^{th }$element in succession is .....?

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

Exam Relevance: AP Statistics, GRE, GMAT, MCAT

Difficulty: Moderate

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

Common Mistakes: A common misunderstanding is confusing systematic sampling with simple random sampling. Simple random sampling involves selecting elements entirely at random, whereas systematic sampling follows a fixed interval after a random start.

Explanations: Systematic sampling involves selecting every nth element from a population after a random start. This method ensures a more structured and systematic approach to sampling compared to simple random sampling, which selects elements entirely at random. The key feature of systematic sampling is the fixed interval, which is maintained throughout the sampling process.

Option Analysis:

Option A: Simple random sampling involves selecting elements entirely at random, without any fixed interval. This does not match the description given in the question.
Option B: Snowball sampling is a non-probability sampling technique where existing study subjects recruit future subjects from among their acquaintances. This does not follow a fixed interval and is not a probability sampling method.
Option C: Stratified sampling involves dividing the population into subgroups (strata) and then sampling from each stratum. This does not involve selecting every nth element in a fixed interval.
Option D: Systematic sampling involves selecting every nth element after a random start, which matches the description given in the question.

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, nonzero chance of being included. This helps ensure that the sample is representative of the entire population.

How does stratified random sampling differ from simple random sampling?

Stratified random sampling involves dividing the population into subgroups (strata) based on certain characteristics, then randomly selecting samples from each stratum. This ensures that specific subgroups are proportionally represented in the sample.

What is cluster sampling and when is it used?

Cluster sampling involves dividing the population into clusters, then randomly selecting entire clusters to be included in the sample. It is often used when the population is large and spread out geographically, making it more practical and cost-effective.

How does systematic sampling work?

Systematic sampling involves selecting every nth member from a list after a random start. This method is useful when the population is large and a simple random sample is difficult to obtain.

What is selection bias and how can it be avoided?

Selection bias occurs when the sample is not representative of the population, leading to skewed results. It can be avoided by using probability sampling methods that ensure each member has an equal chance of being selected.

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