Mathematics for Computer Science Engineers: Sampling

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Questions and Answers

What is a major disadvantage of stratified sampling?

It requires fewer resources than cluster sampling.

It can cause classification errors. (correct)

It allows for larger sample sizes.

It simplifies the sampling frame creation.

When is cluster sampling most appropriately used?

When populations can be easily segmented into similar groups.

When individual members of a population must be sampled.

When populations are already broken up into groups. (correct)

When a small sample size is desired.

Which characteristic is crucial for each cluster in cluster sampling?

Clusters must contain the same number of elements.

Clusters should have no relationship to the overall population.

Clusters must vary widely in their characteristics.

Clusters should be similar to the overall population. (correct)

What can be a consequence of having a large number of strata in stratified sampling?

Potentially larger sample requirements than other methods. Signup and view all the answers

What is one reason that stratified sampling may require more resources?

It requires specific sampling frames for each stratum. Signup and view all the answers

Which method involves selecting entire clusters rather than individuals?

Cluster sampling. Signup and view all the answers

What is a key aspect of cluster sampling in terms of group composition?

Heterogeneous members within each cluster. Signup and view all the answers

What is a potential issue when stratifying variables in stratified sampling?

It may not be related to all variables involved. Signup and view all the answers

Under what conditions can readings from a scale be considered a simple random sample?

If the physical characteristics of the scale remain the same for each weighing. Signup and view all the answers

What is the population in the context of scale readings?

All the readings that the scale could theoretically produce. Signup and view all the answers

Why is cluster sampling recommended when investigating the nutritional status of preschool children?

It allows for easier data collection from geographically dispersed populations. Signup and view all the answers

In the estimation of immunization coverage, what is a benefit of using data from seven children in 30 clusters?

It provides a representative sample of the entire province. Signup and view all the answers

What is the primary characteristic of one-stage cluster sampling?

All members from selected clusters are included. Signup and view all the answers

Which factor does not influence the effectiveness of a sampling method?

The specific time of day when samples are collected. Signup and view all the answers

Which of the following best describes the difference between strata and clusters in sampling?

All strata are included in the sample, while only some clusters are included. Signup and view all the answers

Which statement about two-stage cluster sampling is true?

It involves selecting a subset of members from chosen clusters. Signup and view all the answers

What defines non-probability sampling?

Some units have no chance of being selected. Signup and view all the answers

Which type of sampling is also known as convenience sampling?

Accidental sampling. Signup and view all the answers

What yields the best survey results in stratified sampling?

Elements within strata should be homogeneous. Signup and view all the answers

Which method of cluster sampling involves random selection of clusters followed by member selection?

Two-stage sampling. Signup and view all the answers

What is a major limitation of cluster sampling?

It may not capture the true diversity within the population. Signup and view all the answers

What is a key disadvantage of judgmental sampling?

It is prone to errors in judgment by the researcher. Signup and view all the answers

What is the primary characteristic of quota sampling as compared to stratified sampling?

It uses predetermined characteristics for selection. Signup and view all the answers

When is it appropriate to use quota sampling?

When investigating specific traits of certain subgroups. Signup and view all the answers

In the general procedure of quota sampling, what is the first step?

Divide the population into subgroups. Signup and view all the answers

What is the primary reason to use systematic sampling?

It is effective when project budget is tight and time is limited. Signup and view all the answers

What is a potential limitation of using judgmental sampling in research?

It can affect the study's outcomes significantly. Signup and view all the answers

Which of the following statements about quota sampling is true?

It allows researchers to focus on specific population traits. Signup and view all the answers

In systematic sampling, how is the selection interval 'k' calculated?

k is the population size divided by the sample size. Signup and view all the answers

What is a significant consequence of poor judgment in selection during judgmental sampling?

Higher levels of bias in findings. Signup and view all the answers

Which of the following statements about systematic sampling is false?

All subsets of the same size have equal selection probabilities. Signup and view all the answers

Which method of sampling ensures that specific quotas for subgroups are met?

Quota sampling Signup and view all the answers

Consider a classroom with 64 students, from which 8 students are to be selected using systematic sampling. What would be the sample sequence after randomly selecting the first student as 2?

{2, 10, 18, 26, 34, 42, 50, 58} Signup and view all the answers

How does systematic sampling ensure ease of selection?

It utilizes a structured approach to selecting elements at fixed intervals. Signup and view all the answers

In the example of sampling purchase orders with a total of 10,000 orders needing a sample of 50, what is the first sampled order if you randomly select the 45th order from the first 200?

245 Signup and view all the answers

What is one potential disadvantage of systematic sampling?

It can lead to bias if the population follows a pattern. Signup and view all the answers

Selecting every 4th coin from a set of 20, starting from the 3rd coin, yields which set of coins?

{3, 7, 11, 15, 19} Signup and view all the answers

Study Notes

Sampling Techniques Overview

Different sampling methods provide varied probabilities of selection across population subsets.
Simple random sampling may not be applicable if subsets have unequal selection probabilities.

Systematic Sampling

When to Use: Useful when time and budget constraints exist.
Key Aspect: Select every kth member from the population.
Procedure:
- Assign numbers to population elements.
- Order the population.
- Calculate the selection interval (k = N/n).
- Randomly select the first sample from the initial k members.
- Continuously select subsequent samples at intervals of k.

Systematic Sampling Examples

Classroom Example: From 64 students, select 8 students. (k = 8).
Order of selection: Randomly pick the first student, then every 8th student subsequently.
Purchase Order Example: For 10,000 orders, selecting 50 requires sampling every 200th order.
Coin Selection Example: From 20 coins, 5 must be chosen; selecting every 4th coin after the first.

Advantages of Systematic Sampling

Simplifies the selection process.
Greater precision may lead to smaller sample sizes, reducing costs.

Stratified Sampling Disadvantages

Requires a distinct sampling frame for each stratum.
Potential complications when stratifying variables relate inconsistently to the population.
Often necessitates larger sample sizes for certain designs, increasing time and cost.
Higher risk of classification errors.

Cluster Sampling

Population is divided into non-overlapping clusters, similar to stratified sampling.
Clusters should reflect characteristics of the entire population.
Instead of sampling individuals from each cluster, entire clusters are chosen randomly.
Can subdivide clusters if necessary to achieve an adequate sample size.

Cluster Sampling Procedure

Divide population into clusters.
Randomly select clusters for sampling.
Include all elements or a random selection from the selected clusters.

Cluster Sampling Types

One-stage Sampling: All elements within randomly selected clusters are sampled.
Two-stage Sampling: Randomly select some members from the chosen clusters.

Differences between Stratified and Cluster Sampling

In stratified sampling, all strata are included in the sample; only a subset of clusters is chosen in cluster sampling.
Best results in stratified sampling occur with homogenous elements, while heterogeneous clusters yield better results in cluster sampling.

Non-Probability Sampling

Involves selection where not every member has a chance of being included.
Types include judgmental, snowball, convenience, and quota sampling.

Convenience Sampling

Also known as opportunity sampling; uses readily available subjects.
Researchers choose participants based on accessibility rather than randomness.

Judgmental Sampling: Advantages & Disadvantages

Advantages: Quick, leverages researcher expertise, no specialized statistical knowledge needed, proximate results.
Disadvantages: Subject to researcher bias, low reliability, difficulty in generalizing findings, sample size challenges.

Quota Sampling

Participants selected to satisfy predetermined quotas based on specific characteristics.
Segmentation of the population mirrors stratified sampling but lacks randomness.

Quota Sampling Procedure

Segment population into subgroups.
Determine proportions of these subgroups.
Select samples while maintaining subgroup proportions to complete quotas.

Quota Sampling Example

Selecting coins from a varied set based on specific characteristics, such as multiples of four.

Cluster Sampling Recommendation

Often recommended for surveys assessing undernourished children or immunization rates, as it efficiently uses existing demographic divisions to allocate resources effectively.

Key Points on Sampling Techniques

Each sampling method has its unique characteristics, advantages, and disadvantages, influencing research outcomes and practicality.
Awareness of the context and application of each method is crucial for effective research design and data collection.

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Description

This quiz focuses on systematic sampling methods in the context of Mathematics for Computer Science Engineers. It explains when to use systematic sampling, how to determine selection probabilities, and outlines the general procedure for implementation. Test your understanding of these key concepts and enhance your statistical knowledge.