/*! 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 12 Identify the type of sampling us... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 12

Identify the type of sampling used. A member of Congress wishes to determine her constituency's opinion regarding estate taxes. She divides her constituency into three income classes: low- income households, middle-income households, and upper-income households. She then takes a simple random sample of households from each income class.

Short Answer

Expert verified
Stratified sampling

Step by step solution

01

Title - Understanding the Sampling Method

Identify the process used to obtain the samples. The text states that the member of Congress divides her constituency into three income classes and then takes a simple random sample from each class.
02

Title - Recognizing Sampling Techniques

Review different sampling methods: simple random sampling, stratified sampling, systematic sampling, cluster sampling, and convenience sampling.
03

Title - Matching Techniques with the Description

Relate the steps described in the problem to the characteristics of the sampling techniques. The method described involves dividing the population into different strata (income classes) and then performing random sampling within each stratum.
04

Title - Identifying the Correct Sampling Method

Since the process involves dividing the constituency into income classes (strata) and then taking random samples within each class, this method aligns with stratified sampling.

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 91影视!

Key Concepts

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

Sampling Methods
Sampling methods are techniques used to select a subset of individuals from a population to estimate characteristics of the whole population. Proper sampling techniques ensure that the samples accurately represent the population for credible analysis and conclusions.

Some common sampling methods include:

  • Simple Random Sampling: Every member of the population has an equal chance of being selected. It's like a lottery where everyone has an equal shot.
  • Stratified Sampling: The population is divided into subgroups, or 'strata,' and random samples are taken from each stratum. This ensures representation from all the crucial segments of the population.
  • Systematic Sampling: Selecting every nth individual from a list of the population. It's simpler but can introduce bias if there's a hidden pattern in the list.
  • Cluster Sampling: The population is divided into clusters, a few clusters are randomly chosen, and then all members of those clusters are sampled. It's efficient but less precise if clusters vary widely.
  • Convenience Sampling: Simply selecting individuals who are easiest to reach. This is the least reliable as it often doesn't represent the whole population.
Random Sampling
Random sampling is a cornerstone of statistical sampling methods ensuring each member of a population has an equal chance of being included in the sample. This minimizes bias and helps in drawing accurate conclusions.

In practice, random sampling can be performed in multiple ways:

  • Lottery Method: Names or numbers are written on slips of paper, mixed up, and drawn at random. This is simple but might not be feasible for large populations.
  • Random Number Tables: Tables with randomly generated numbers can be used to select members of the population.
  • Computer-Generated Random Numbers: Modern software can create random numbers, making the selection process fast and reliable.


It's important to note that even in methods like stratified sampling, the elements within each stratum are selected randomly to maintain the integrity of the sample.
Strata in Statistics
In statistics, a 'stratum' (plural 'strata') refers to a subgroup of the population that shares certain characteristics. Stratified sampling involves these well-defined strata to provide more accurate and reliable results.

Key aspects of strata in statistics:

  • Definition: Strata are defined based on specific attributes relevant to the study, such as income level, age group, geographic region, etc.
  • Homogeneity within Strata: Members of each stratum are similar concerning specific characteristics. This homogeneity helps in reducing variability within the strata, thereby improving the precision of the estimates.
  • Heterogeneity Between Strata: The strata differ significantly from one another based on the defining characteristics. This distinction helps in capturing the diversity of the population more effectively.
  • Proportional Representation: When conducting stratified sampling, the sample sizes from each stratum can be proportional to the strata's sizes in the population. This ensures each stratum is fairly represented.

    An example from the exercise: The Congress member divides the constituency into 'low-income households', 'middle-income households', and 'upper-income households', making each income class a stratum. Random samples are then taken within each income class to ensure all income levels are represented in the final analysis.

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

Researchers wanted to evaluate whether ginkgo, an over-the-counter herb marketed as enhancing memory, improves memory in elderly adults as measured by objective tests. To do this, they recruited 98 men and 132 women older than 60 years and in good health. Participants were randomly assigned to receive ginkgo, \(40 \mathrm{mg} 3\) times per day, or a matching placebo. The measure of memory improvement was determined by a standardized test of learning and memory. After 6 weeks of treatment, the data indicated that ginkgo did not increase performance on standard tests of learning, memory, attention, and concentration. These data suggest that, when taken following the manufacturer's instructions, ginkgo provides no measurable increase in memory or related cognitive function to adults with healthy cognitive function. (Source: "Ginkgo for Memory Enhancement," Paul R. Solomon, et. al.; Journal of the American Medical Association 288(2002): 835-840)$ (a) What type of experimental design is this? (b) What is the population being studied? (c) What is the response variable in this study? (d) What is the factor? What are the treatments? (e) Identify the experimental units. (f) Draw a diagram similar to Figure 6 or 7 to illustrate the design.

The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4,502 employees at the company and wants to conduct a systematic sample. (a) Determine \(k\) if the sample size is \(50 .\) (b) Determine the individuals who will be administered the survey. More than one answer is possible.

A research objective is presented. For each research objective, identify the population and sample in the study. A large community college has noticed that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks this question: How many hours per week do you work?

Researchers wish to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of salt consumption. It is also known that there is quite a bit of person-to-person variability as far as the ability of the body to process and eliminate salt. However, no method exists for identifying individuals who have a higher ability to process salt. The U.S. Department of Agriculture recommends that daily intake of salt should not exceed 2400 mg. The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design. (a) What is the response variable in the study? (b) Name three factors that have been identified. (c) For each factor identified, determine whether the variable can be controlled, cannot be controlled, or should be manipulated. If a factor cannot be controlled, what should be done to reduce variability in the response variable? (d) How many treatments would you recommend? Why?

The city of Naperville is considering the construction of a new commuter rail station. The city wishes to survey the residents of the city to obtain their opinion regarding the use of tax dollars for this purpose. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation
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.