/*! 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 23 In Problems 11-22, identify the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 23

In Problems 11-22, identify the type of sampling used. A salesperson obtained a systematic sample of size 20 from a list of 500 clients. To do so, he randomly selected a number from 1 to 25 , obtaining the number \(16 .\) He included in the sample the 16 th client on the list and every 25 th client thereafter. List the numbers that correspond to the 20 clients selected.

Short Answer

Expert verified
16, 41, 66, 91, 116, 141, 166, 191, 216, 241, 266, 291, 316, 341, 366, 391, 416, 441, 466, 491

Step by step solution

01

Understand Systematic Sampling

Systematic sampling involves selecting every k-th item from a list after a random start point is determined.
02

Identify Random Start Point

The problem states that a random number between 1 and 25 was chosen, which is 16.
03

Determine Sampling Interval

The interval for systematic sampling is every 25th client.
04

Generate the Sequence of Client Numbers

Start at 16 and add 25 to get the next client number. Continue this step until 20 clients are selected: 16, 41, 66, 91, 116, 141, 166, 191, 216, 241, 266, 291, 316, 341, 366, 391, 416, 441, 466, 491

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 essential in statistics and research. They are techniques used to select individuals or items for analysis from a larger group, known as the population. Understanding different sampling methods helps ensure the data collected is representative and unbiased. One common method is systematic sampling. Imagine you have a list of 500 clients and want to survey a smaller group of 20. Systematic sampling allows you to select every k-th client from your list, providing an even spread across the entire population. This method is efficient and easy to implement.
random start point
A random start point is crucial in systematic sampling to ensure randomness and reduce bias. It involves selecting a random position in your list to begin sampling. For example, let鈥檚 say a salesperson randomly selects a number from 1 to 25. In our exercise, the chosen number is 16. This random start point means the salesperson will select the 16th client first. Ensuring this randomness helps maintain the integrity of the sample, avoiding systematic bias that could skew results.
sampling interval
The sampling interval is another key component in systematic sampling. It is the fixed gap or distance between each sampled item after the random start point. In our exercise, the interval is every 25th client. Starting from the 16th client, the salesperson then adds 25 to the position to find the next client: 16, 41, 66, and so on. This interval ensures a uniform distribution of sampled clients, enhancing the reliability of the sample. By clearly defining the interval, the process becomes predictable and replicable.
sequence generation
Sequence generation involves creating the list of selected items based on the start point and interval. For systematic sampling, begin with your random start point and add the sampling interval repeatedly. In the exercise, starting at client 16 and adding 25 each time, we get the sequence: 16, 41, 66, 91, 116, 141, 166, 191, 216, 241, 266, 291, 316, 341, 366, 391, 416, 441, 466, 491. This sequence generation is straightforward yet powerful, ensuring that the 20 clients sampled are evenly spread and truly representative of the larger group.

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

Gallup News Service conducted a survey of 1017 American adults aged 18 years or older, September \(4-7,2014 .\) The respondents were asked, "Of every tax dollar that goes to the federal government in Washington, D.C. how many cents of each dollar would you say are wasted?" Of the 1017 individuals surveyed, \(35 \%\) indicated that 51 cents or more is wasted. Gallup reported that \(35 \%\) of all adult Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of \(4 \%\) and a \(95 \%\) level of confidence. (a) What is the research objective? (b) What is the population? (c) What is the sample? (d) List the descriptive statistics. (e) What can be inferred from this survey?

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. A magazine is conducting a study on the effects of infidelity in a marriage. The editors randomly select 400 women whose husbands were unfaithful and ask, "Do you believe a marriage can survive when the husband destroys the trust that must exist between husband and wife?"

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.

Is a television (TV) in the bedroom associated with obesity? Researchers questioned 379 twelve-year old adolescents and concluded that the body mass index (BMI) of the adolescents who had a TV in their bedroom was significantly higher than the BMI of those who did not have a TV in their bedroom. Source: Christelle Delmas, Carine Platat, Brigette Schweitzer, Aline Wagner, Mohamed Oujaa, and Chantal Simon. "Association Between Television in Bedroom and Adiposity Throughout Adolescence," Obesity, \(15: 2495-2503,2007\) (a) Why is this an observational study? What type of observational study is this? (b) What is the response variable in the study? What is the explanatory variable? (c) Can you think of any lurking variables that may affect the results of the study? (d) In the report, the researchers stated, "These results remain significant after adjustment for socioeconomic status." What does this mean? (e) Can we conclude that a television in the bedroom causes a higher body mass index? Explain.

Classify the variable as qualitative or quantitative. Number of siblings
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.