/*! 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 3 \(A\) large retailer prepares it... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 3

\(A\) large retailer prepares its customers' monthly credit card bills using an automatic machine that folds the bills, stuffs them into envelopes, and seals the envelopes for mailing. Are the envelopes completely sealed? Inspectors choose 40 envelopes at random from the 1000 stuffed each hour for visual inspection. Identify the population and the sample.

Short Answer

Expert verified
Population: 1000 envelopes stuffed each hour; Sample: 40 envelopes inspected.

Step by step solution

01

Define the Population

To identify the population, we need to determine the entire group being studied. In this exercise, the population refers to all of the envelopes that are stuffed each hour by the automatic machine. Specifically, this is the total of 1000 envelopes stuffed each hour.
02

Define the Sample

The sample is a subset of the population that is actually observed or inspected. In this exercise, the sample consists of the 40 envelopes that inspectors choose at random from the 1000 envelopes stuffed each hour for visual inspection.

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.

Population
In statistics, the term "population" refers to the complete set of elements or members that you are interested in studying. In the context of the exercise, the population comprises all the envelopes that are stuffed each hour by the machine. That means:
  • The population includes all 1000 envelopes processed in that timeframe.
  • This group is what we want to learn about or draw conclusions from.
  • In practical terms, managing a population of this size can often be challenging and resource-intensive.
Understanding the population is crucial because it represents the entire domain from which we hope to extrapolate meaningful insights. Upon examining a properly defined population, statistical inferences can be made to understand broader trends, product quality, or operational efficiency. In this exercise, the population is every envelope produced by the machine for each operational hour.
Sample
A sample is a smaller, manageable number of subjects that are chosen from the population. In our exercise, the sample includes only the 40 envelopes that inspectors randomly pick from the set of 1000 envelopes produced each hour. Here's why samples are key:
  • They allow us to gather data and make inferences about the population without needing to examine every single member.
  • Studying a sample is often more practical and less costly than attempting to survey an entire population.
  • It's important for the sample to be representative of the population to ensure accurate conclusions.
Choosing a good, representative sample helps us to gain insights without the impossible task of examining every single envelope. It allows a streamlined assessment of whether the envelopes are adequately sealed, providing a snapshot of the overall production quality.
Random Selection
Random selection is a method used to ensure that every member of a population has an equal chance of being included in the sample. In the given exercise, inspectors utilize random selection when choosing their sample of 40 envelopes from the 1000 produced each hour. This technique offers several benefits:
  • It minimizes selection bias, providing a fair representation of the entire population.
  • Random selection is a foundational aspect of ensuring statistical validity.
  • It assists in producing more reliable and generalizable results.
When inspectors select envelopes at random, they prevent any unintended preference or bias that could influence or skew the inspection results. Random selection is crucial in accurately assessing the quality of envelope sealing across the board, thus maintaining the integrity of the sampling process.

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

Will cash bonuses speed the return to work of unemployed people? A state department of labor notes that last year 68 % of people who filed claims for unemployment insurance found a new job within 15 weeks. As an experiment, this year the state offers 500 to people filing unemployment claims if they find a job within 15 weeks. The percent who do so increases to 77 %. What flaw in the design of this experiment makes it impossible to say whether the bonus really caused the increase? Explain.

At a party there are 30 students over age 21 and 20 students under age 21 . You choose at random 3 of those over 21 and scparately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed. Why is your sample not an SRS?

A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They use an aerial map to divide the forest into 200 equal-sized rectangles. Then they choose a random sample of 20 rectangles and examine every tree that's in one of those rectangles. (a) What is the name for this kind of sampling method? (b) Give a possible reason why the lumber company chose this method.

\(A\) study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about scat belt use. In all, \(75 \%\) said they always used seat belts, yet only \(61.5 \%\) were wearing seat belts when they pulled into the store parking lots. \({ }^{17}\) Fexplain the reason for the bias observed in responses to the survey. Do you expect bias in the same direction in most surveys about seat belt use?

To investigate whether standing up while studying affects performance in an algebra class, a teacher assigns half of the 30 students in his class to stand up while studying and assigns the other half to not stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. The teacher does the same for the next two highest-scoring students and continues in this manner until each student is assigned a treatment. Which of the following best describes this plan? (a) This is an observational study. (b) This is an experiment with blocking. (c) This is a completely randomized experiment. (d) This is a stratified random sample. (e) This is a cluster sample.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and 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.