/*! 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 6 When taking a systematic random ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

When taking a systematic random sample of size \(n,\) every group of size \(n\) from the population has the same chance of being selected.

Short Answer

Expert verified
Choose a random starting point, then select every k-th element where k = N/n.

Step by step solution

01

- Define Systematic Random Sampling

Systematic random sampling involves selecting every k-th element from a population list, where k is a constant. To determine k, divide the population size (N) by the sample size (n): \[ k = \frac{N}{n} \]
02

- Identify Sample Size and Population Size

Identify the total population size (N) and the desired sample size (n). For example, if the population size is 100 and the sample size is 10, then N = 100 and n = 10.
03

- Calculate the Sampling Interval

Using the formula from step 1, calculate the sampling interval (k). For N = 100 and n = 10: \[ k = \frac{100}{10} = 10 \]
04

- Select a Random Starting Point

Choose a random starting point from the first k elements in the population. For example, if k = 10, select a random number between 1 and 10.
05

- Select Every k-th Element

Starting from the randomly selected point, select every k-th element to form the sample. For instance, if the random starting point is 3 and k = 10, the sample elements would be at positions 3, 13, 23, etc.
06

- Verify Equal Selection Probability

To ensure every group of size n has an equal chance of being selected, verify that the population is arranged in a way that each k-th element represents a balanced view of the population without clustering specific segments.

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 Techniques
Sampling techniques are methods used to select a subset of individuals from a larger population to estimate characteristics of the whole population.
There are many sampling techniques, including but not limited to:
  • Simple random sampling: Each member of the population has an equal probability of being included in the sample.
  • Systematic random sampling: A method where you select every k-th element from a list of the population.
  • Stratified sampling: The population is divided into subgroups (strata) based on specific characteristics. Samples are then taken from each strata.
  • Cluster sampling: The population is divided into clusters, and randomly selected clusters are sampled entirely.
In systematic random sampling, the steps involve calculating the interval (k), selecting a random starting point, and continuing with every k-th element. This method ensures the sample is spread evenly across the population. Understanding different sampling techniques helps in choosing the appropriate method for various research scenarios.
Sample Size Determination
Determining the sample size is a crucial step in any statistical study. The sample size determines the accuracy and reliability of the results. Several factors influence the determination of the sample size, including:
  • Population size (N): The total number of individuals or elements in the population.
  • Desired confidence level: Typically set at 95% or 99%, indicating how confident we are that the sample represents the population.
  • Margin of error: The range within which we expect the true population parameter to lie, commonly set at 5% or 1%.
  • Variability in the population: Higher variability requires a larger sample size to accurately estimate the population characteristics.
In systematic random sampling, the sample size (n) is determined first, followed by the calculation of the sampling interval (k) using the formula \(k = \frac{N}{n}\). This ensures every part of the population is equally represented, and the sample size is manageable and adequate for analysis.
Probability Sampling Methods
Probability sampling methods are techniques where every member of the population has a known, non-zero chance of being selected. These methods are essential for ensuring the sample accurately represents the population. Key probability sampling methods include:
  • Simple random sampling: Every individual has an equal chance of being selected. Commonly used for its simplicity and fairness.
  • Systematic random sampling: Involves selecting every k-th element, reducing time and effort compared to simple random sampling while maintaining randomness.
  • Stratified sampling: Divides the population into strata and ensures each subgroup is represented proportionally in the sample, enhancing accuracy for diverse populations.
  • Cluster sampling: Involves selecting entire clusters randomly and then sampling all individuals within these clusters. Useful for large, geographically dispersed populations.
Systematic random sampling is a type of probability sampling where the interval (k) is calculated, and a random starting point is chosen. It maintains the randomness and represents the population fairly, making it an effective method for various types of research studies.

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

In Problems 11-22, identify the type of sampling used. To obtain students' opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one of their classes. Twenty-three faculty members volunteered. Each faculty member gave the survey to all the students in one course of their choosing. Would this sampling method be considered a cluster sample? Why or why not?

Contrast the differences between qualitative and quantitative variables.

Research the polling done by George Gallup in the 1936 presidential election. Write a report on your findings and include information about the sampling technique and sample size. Next, research the polling done by Gallup for the 1948 presidential election. Did Gallup accurately predict the outcome of the election? What lessons were learned by Gallup?

A researcher has recruited 20 volunteers to participate in a study. The researcher wishes to measure the effect of alcohol on an individual's reaction time. The 20 volunteers are randomly divided into two groups. Group 1 serves as a control group in which participants drink four 1-ounce cups of a liquid that looks, smells, and tastes like alcohol in 15 -minute increments. Group 2 serves as an experimental group in which participants drink four 1 -ounce cups of 80 -proof alcohol in 15 -minute increments. After drinking the last 1 -ounce cup, the participants sit for 20 minutes. After the 20 -minute resting period, the reaction time to a stimulus is measured. (a) What type of experimental design is this? (b) Use Table I in Appendix A or a random-number generator to divide the 20 volunteers into groups 1 and 2 by assigning the volunteers a number between 1 and \(20 .\) Then randomly select 10 numbers between 1 and \(20 .\) The individuals corresponding to these numbers will go into group \(1 .\)

A research objective is presented. For each, identify the population and sample in the study. A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

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.