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Unit Ii Research Aptitude
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Sampling – Quiz 91
Sampling Quiz 91 (10 MCQs)
This set of Multiple Choice Questions evaluates understanding of random selection, equal probability, unbiased sampling, systematic sampling, and interval determination. It covers concepts such as population vs. sample, population definition, sampling frame, and representativeness. The questions also assess knowledge of sampling methods, including simple random sampling, stratified sampling, and the importance of avoiding sampling bias.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
Where the sample chosen is not representative of the population-it is
A) Secondary.
B) Sample.
C) Bias.
D) Parameter.
Show Answer
Correct Answer:
Correct answer is: (C) Bias.
Exam Relevance:
AP Statistics, GRE, GMAT, SAT
Difficulty:
Moderate
Concept notes:
In sampling, bias occurs when the sample does not accurately represent the population, leading to skewed or misleading results.
Common Mistakes:
A common misunderstanding is that any sample chosen is representative of the population, which is not always true.
Explanations:
When a sample is not representative of the population, it introduces bias. This means that the sample does not accurately reflect the characteristics of the entire population, leading to potential errors in the conclusions drawn from the sample data.
Option Analysis:
Option A:
Secondary data refers to data that has already been collected for a different purpose and is reused for the current study. It is not related to the concept of bias in sampling.
Option B:
Sample refers to a subset of the population used for analysis. While a sample is necessary for sampling, the question specifically addresses the issue of non-representativeness, which is a form of bias.
Option C:
Bias is the correct term for when a sample does not accurately represent the population, leading to skewed results.
Option D:
Parameter refers to a numerical characteristic of a population. It is not related to the issue of non-representative sampling.
2.
If the entire population is surveyed, the type of survey is a/an:
A) Stratified Sampling.
B) Random Sampling.
C) Population Sampling.
D) Census.
Show Answer
Correct Answer:
Correct answer is: (D) Census.
Exam Relevance:
AP Statistics, GRE, GMAT, Census Bureau Exams
Difficulty:
Easy
Concept notes:
A census is a survey that collects data from every member of a population.
Common Mistakes:
A common misunderstanding is that a census is a type of sampling method, but it is not. Sampling involves selecting a subset of the population, whereas a census involves surveying the entire population.
Explanations:
A census involves collecting data from every individual in the population, which means that the entire population is surveyed. This is different from sampling methods like stratified or random sampling, which only survey a portion of the population.
Option Analysis:
Option A:
Stratified Sampling involves dividing the population into subgroups and then sampling from each subgroup. This is not the same as surveying the entire population.
Option B:
Random Sampling involves selecting a subset of the population randomly. This is not the same as surveying the entire population.
Option C:
Population Sampling is not a standard term. It might be confused with the idea of surveying the entire population, but it is not a recognized method.
Option D:
Census involves surveying the entire population, which matches the description in the question.
3.
A gaming website wanted to find out which console its visitors owned. Which choice BEST represents a population?
A) Visitors with an 'e' in their user name.
B) Visitors to the 3DS section.
C) Visitors over 22.
D) All the website visitors.
Show Answer
Correct Answer:
Correct answer is: (D) All the website visitors.
Exam Relevance:
AP Statistics, GRE, GMAT, SAT
Difficulty:
Moderate
Concept notes:
In sampling, the population is the complete set of individuals or items that are the subject of study. The goal is to gather data that represents the entire group.
Common Mistakes:
A common mistake is to choose a subset of the population that may not be representative, such as visitors with a specific characteristic or those visiting a specific section of the website.
Explanations:
The population in this context is all the website visitors because it includes every individual who could potentially be surveyed. This ensures that the sample taken from this population is representative of the entire group of visitors, not just a subset with specific characteristics.
Option Analysis:
Option A:
Visitors with an 'e' in their user name is a subset and not the entire population.
Option B:
Visitors to the 3DS section is a subset and not the entire population.
Option C:
Visitors over 22 is a subset and not the entire population.
Option D:
All the website visitors represents the entire population.
4.
The first step in sampling design is:
A) Collecting data.
B) Defining population.
C) Writing conclusion.
D) Interpreting results.
Show Answer
Correct Answer:
Correct answer is: (B) Defining population.
Exam Relevance:
AP Statistics, GRE, GMAT, Research Methods Exams
Difficulty:
Easy
Concept notes:
The first step in sampling design is to clearly define the population from which the sample will be drawn.
Common Mistakes:
A common misunderstanding is to start with data collection without first defining the population, which can lead to sampling bias and inaccurate results.
Explanations:
Defining the population is crucial because it establishes the scope and boundaries of the study. It ensures that the sample accurately represents the group of interest, which is essential for valid and reliable results.
Option Analysis:
Option A:
Collecting data is a subsequent step after defining the population and designing the sampling method.
Option B:
Defining the population is the first step in sampling design, as it sets the foundation for the entire study.
Option C:
Writing conclusions comes after data analysis and is not part of the initial sampling design process.
Option D:
Interpreting results is a later step in the research process, following data collection and analysis.
5.
Interview every 10th student who enters the school in the morning. Determine the sampling method used.
A) Simple random sampling.
B) Cluster sampling.
C) Systematic sampling.
D) Convenience sampling.
Show Answer
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 member of the population after a random start. In this case, every 10th student is selected, which fits the definition of systematic sampling.
Common Mistakes:
A common mistake is confusing systematic sampling with simple random sampling. Simple random sampling requires each individual to have an equal chance of being selected, without a specific pattern.
Explanations:
Systematic sampling is used when the population is large and a simple random sample is difficult to obtain. By selecting every 10th student, the method ensures a consistent and systematic approach to sampling. This method is efficient and can provide a representative sample if the population is homogeneous and there is no periodic pattern in the population that aligns with the sampling interval.
Option Analysis:
Option A:
Simple random sampling involves selecting individuals completely at random, without any specific pattern. This does not apply here as the students are selected based on a fixed interval.
Option B:
Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This does not apply here as individual students are selected, not clusters.
Option C:
Systematic sampling involves selecting every kth member of the population after a random start. This matches the scenario where every 10th student is selected.
Option D:
Convenience sampling involves selecting individuals based on convenience or ease of access. This does not apply here as the selection is based on a fixed interval, not convenience.
6.
What kind of sample technique is the following:Question 90 employees chosen at random.
A) Convenience Sampling.
B) Simple Random Sampling.
C) Systematic Sampling.
D) Sample.
Show Answer
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 method 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 the sample is chosen based on ease of access rather than random selection.
Explanations:
In Simple Random Sampling, each of the 90 employees has an equal and independent chance of being chosen. This ensures that the sample is representative of the entire population, as there is no bias in the selection process.
Option Analysis:
Option A:
Convenience Sampling involves selecting individuals based on ease of access, which is not the case here.
Option B:
Simple Random Sampling is the correct choice as it involves selecting individuals randomly with equal probability.
Option C:
Systematic Sampling involves selecting individuals at regular intervals from a list, which is not described in the question.
Option D:
"Sample" is too general and does not specify the method of selection.
7.
Identify the type of sampling technique"A researcher who is studying the effects of educational attainment on promotion conducted a survey of 50 randomly selected workers from each of these categories:high school graduate, with undergraduate degrees, with master's degree, and with doctoral degree."
A) Simple Random Sampling.
B) Systematic Sampling.
C) Stratified Sampling.
D) Cluster Sampling.
Show Answer
Correct Answer:
Correct answer is: (C) Stratified Sampling.
Exam Relevance:
AP Statistics, GRE, GMAT, MCAT
Difficulty:
Moderate
Concept notes:
Stratified sampling involves dividing the population into distinct subgroups (strata) based on specific characteristics and then randomly sampling from each subgroup.
Common Mistakes:
A common misunderstanding is confusing stratified sampling with simple random sampling, where the entire population is treated as a single group without any subgroups.
Explanations:
In this scenario, the population of workers is divided into distinct strata based on their educational attainment levels: high school graduate, with undergraduate degrees, with master's degree, and with doctoral degree. The researcher then randomly selects 50 workers from each stratum. This method ensures that each subgroup is adequately represented in the sample, which is the essence of stratified sampling.
Option Analysis:
Option A:
Simple Random Sampling involves selecting a sample from the entire population without any subgroup division. This does not apply here as the population is divided into strata.
Option B:
Systematic Sampling involves selecting every nth member from a list after a random start. This does not apply here as the population is divided into strata and random sampling is done within each stratum.
Option C:
Stratified Sampling involves dividing the population into strata and then randomly sampling from each stratum. This matches the scenario described.
Option D:
Cluster Sampling involves dividing the population into clusters and then randomly selecting entire clusters. This does not apply here as the population is divided into strata and random sampling is done within each stratum.
8.
A ..... is a sub-set of the population.
A) Subject.
B) Sample.
C) Population.
D) Group.
Show Answer
Correct Answer:
Correct answer is: (B) Sample.
Exam Relevance:
AP Statistics, GRE, GMAT, SAT
Difficulty:
Easy
Concept notes:
A sample is a subset of the population used for statistical analysis.
Common Mistakes:
A common misunderstanding is confusing a sample with the entire population.
Explanations:
In sampling, a sample is defined as a subset of the population. This subset is used to make inferences about the entire population. The sample should be representative of the population to ensure accurate conclusions.
Option Analysis:
Option A:
A subject is an individual or entity being studied, not a subset of the population.
Option B:
A sample is a subset of the population used for analysis.
Option C:
A population is the entire group of interest, not a subset.
Option D:
A group is a collection of individuals, but it does not necessarily imply a subset for analysis.
9.
Systematic sampling involves selecting samples every nth member of the population. If the population size is 75 and the sample size is 25, what is the interval for selection?
Show Answer
Correct Answer:
Correct answer is: (A) 3.
Exam Relevance:
AP Statistics, GRE, GMAT, SAT
Difficulty:
Easy
Concept notes:
In systematic sampling, the interval for selection is calculated by dividing the population size by the sample size.
Common Mistakes:
A common mistake is to misinterpret the formula or to use the wrong values for the population size and sample size.
Explanations:
To find the interval for selection in systematic sampling, we use the formula:
\[ \text{Interval} = \frac{\text{Population Size}}{\text{Sample Size}} \]
Given the population size is 75 and the sample size is 25, we calculate:
\[ \text{Interval} = \frac{75}{25} = 3 \]
Thus, the interval for selection is 3.
Option Analysis:
Option A:
Correct. The interval is 3.
Option B:
Incorrect. The interval is not 5.
Option C:
Incorrect. The interval is not 2.
Option D:
Incorrect. The interval is not 10.
10.
A simple random and systematic sample are types of
A) Convenience samples.
B) Biased samples.
C) Unfair samples.
D) Unbiased samples.
Show Answer
Correct Answer:
Correct answer is: (D) Unbiased samples.
Exam Relevance:
AP Statistics, IB Mathematics, GRE, GMAT
Difficulty:
Easy
Concept notes:
Simple random sampling and systematic sampling are both methods designed to ensure that every member of the population has an equal chance of being selected, thereby reducing bias.
Common Mistakes:
A common misunderstanding is that convenience samples or biased samples are also types of random sampling. However, convenience samples are not random and can introduce significant bias.
Explanations:
Simple random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being chosen. Systematic sampling involves selecting individuals at regular intervals from a list or sequence. Both methods aim to minimize bias and ensure that the sample is representative of the population.
Option Analysis:
Option A:
Convenience samples are not random and can introduce bias, so they are not unbiased samples.
Option B:
Biased samples are, by definition, not unbiased, so they do not fit the description.
Option C:
Unfair samples are also biased and do not represent the population accurately, so they are not unbiased samples.
Option D:
Simple random and systematic samples are designed to be unbiased, ensuring that each member of the population has an equal chance of being selected.
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Frequently Asked Questions
What is the main purpose of sampling in research?
The main purpose of sampling in research is to select a subset of the population that accurately represents the entire population, allowing researchers to make inferences about the whole group based on the sample.
How does simple random sampling ensure unbiased results?
Simple random sampling ensures unbiased results by giving every member of the population an equal probability of being selected, which minimizes sampling bias and helps create a representative sample.
What is the difference between a census and a sample survey?
A census collects data from every member of the population, while a sample survey collects data from a subset of the population. Surveys are often used when a census is impractical due to time, cost, or other constraints.
How does stratified sampling differ from simple random sampling?
Stratified sampling divides the population into subgroups (strata) based on specific characteristics, and then a random sample is taken from each stratum. This method ensures that all subgroups are represented in the sample, unlike simple random sampling which does not consider subgroup characteristics.
What is the importance of defining the population in sampling?
Defining the population is crucial because it determines the scope of the study and ensures that the sample accurately reflects the characteristics of the group being studied. A well-defined population helps in selecting an appropriate sampling method and achieving valid results.