/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 Explain the difference between a... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Explain the difference between a stratified sample and a cluster sample.

Short Answer

Expert verified
Stratified sampling divides the population into subgroups and samples each, while cluster sampling selects entire clusters randomly.

Step by step solution

01

Understanding Stratified Sampling

In stratified sampling, the population is divided into distinct subgroups called 'strata' that share similar characteristics. Each strata is then randomly sampled to ensure representation across the whole population. This method is used to highlight differences between groups.
02

Understanding Cluster Sampling

In cluster sampling, the population is divided into clusters (usually geographically). A few entire clusters are then randomly selected, and all individuals within those clusters are surveyed. This method is generally used for practicality and cost-effectiveness.
03

Key Differences

Stratified sampling ensures representation from each subgroup by sampling each stratum, while cluster sampling involves randomly selecting entire clusters and surveying every member of those clusters. Stratified sampling focuses on the differences between subgroups, while cluster sampling often focuses on logistical simplicity.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stratified Sampling
Stratified sampling is a powerful technique used in statistics to ensure that different subgroups within a population are adequately represented in the sample. The process begins by dividing the population into distinct subgroups, known as 'strata', that share specific characteristics. These strata can be based on attributes like age, gender, income levels, or other significant factors. Once these strata are defined, a random sample is taken from each of them.
This approach ensures that the sample reflects the diversity of the population, which helps in understanding the variations among different subgroups more precisely. Stratified sampling is particularly useful when researchers aim to capture specific insights or differences between the distinct groups within the population.
Overall, this method enhances the accuracy and credibility of conclusions made from the data, as each group within the population is proportionately represented.
Cluster Sampling
Cluster sampling stands out as an efficient method, especially when dealing with large and geographically dispersed populations. Here, the population is divided into clusters, which are usually geographically defined, such as cities, schools, or neighborhoods. Instead of sampling individuals across these clusters, entire clusters are chosen at random.
All individuals within the selected clusters are then included in the sample. This method of sampling is favored for its practicality and cost-effectiveness, as it reduces the need for extensive travel and logistical planning. However, it's important to note that while cluster sampling may save resources, it might also introduce sampling bias if the selected clusters are not representative of the population as a whole.
This is why careful consideration must be made when defining and selecting clusters, ensuring they are as homogeneous as possible and truly reflective of the broader population.
Population Subgroups
Population subgroups are essential in statistical sampling. They refer to smaller, defined sections of a larger population that share certain characteristics. Identifying these subgroups allows researchers to focus on particular segments, which can lead to more detailed and nuanced insights.
Subgroups can be based on demographic factors like age, income level, education, or lifestyle, among others. The ultimate goal of creating these subgroups is to ensure that each section of the population is represented in the analysis.
Whether applying stratified or cluster sampling, acknowledging and understanding these subgroups help in structuring a survey or study that accurately reflects the dynamics and diversity of the entire population.
Random Sampling
Random sampling is one of the fundamental principles in statistics, aiming to give each member of the population an equal chance of being chosen. This method minimizes bias and ensures that the results are more likely to reflect the true characteristics of the entire population.
When implementing random sampling in the context of stratified sampling, random samples are drawn from each defined stratum. In cluster sampling, random selection is used to choose which clusters will be surveyed.
Regardless of the sampling technique chosen, the random nature is crucial to maintaining the integrity and credibility of the research findings. It eliminates favoritism in sample selection and helps create a balanced and representative dataset.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the difference between a parameter and a statistic?

Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio. (a) Salesperson's performance: below average, average, above average (b) Price of company's stock (c) Names of new products (d) Temperature \(\left({ }^{\circ} \mathrm{F}\right)\) in CEO's private office (e) Gross income for each of the past 5 years (f) Color of product packaging

Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies? (a) An analysis of a sample of 31,000 patients from New York hospitals suggests that the poor and the elderly sue for malpractice at one-fifth the rate of wealthier patients (Journal of the American Medical Association). (b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight. (c) A study of all league football scores attained through touchdowns and field goals was conducted by the National Football League to determine whether field goals account for more scoring events than touchdowns (USA Today). (d) An Australian study included 588 men and women who already had some precancerous skin lesions. Half got a skin cream containing a sunscreen with a sun protection factor of 17 ; half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer new precancerous skin lesions (New England Journal of Medicine).

Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class. (a) Explain why the first four students walking into the classroom would not necessarily form a random sample. (b) Explain why four students coming in late would not necessarily form a random sample. (c) Explain why four students sitting in the back row would not necessarily form a random sample. (d) Explain why the four tallest students would not necessarily form a random sample.

You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students. (a) Give some instructions for weighing the backpacks. Include unit of measure, accuracy of measure, and type of scale. (b) Do you think each student asked will allow you to weigh his or her backpack? (c) Do you think telling students ahead of time that you are going to weigh their backpacks will make a difference in the weights?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.