/*! 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 A corporation employs 2000 male ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 23

A corporation employs 2000 male and 500 female engineers. A stratified random sample of 200 male and 50 female engineers gives cach engineer 1 chance in 10 to be chosen. This sample design gives every individual in the population the same chance to be chosen for the sample. Is it an SRS? Explain your answer.

Short Answer

Expert verified
No, it's not an SRS because it's stratified, not offering equal sample combinations.

Step by step solution

01

Understand Stratified Sampling

In stratified sampling, the population is divided into subgroups, called strata, that share similar characteristics. Samples are then drawn from each stratum. Here, the engineers are divided by gender into two strata: male and female.
02

Evaluate Individual Probability

In the given problem, each male engineer has a 1 in 10 chance of being chosen, and each female engineer also has a 1 in 10 chance. This maintains the same probability for every individual regardless of their subgroup.
03

Define Simple Random Sampling (SRS)

A Simple Random Sample (SRS) means every possible sample of a certain size has an equal chance of being chosen. This usually implies random selection from the entire population without regard to subgroups.
04

Compare to SRS

Since the sample ensures equal probability within each subgroup but has predetermined quotas (200 males, 50 females), not every possible combination of individuals from the entire group could be selected. This means it does not meet the SRS requirement.

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.

Simple Random Sample (SRS)
A Simple Random Sample (SRS) is a fundamental sampling method in statistics. In SRS, every member of the entire population has an equal chance of being selected, without being confined by constraints like subgroups.
For example, imagine you have a bag of marbles of different colors; if you blindly pick a marble, each one has an equal probability of being chosen. This illustrates the essence of SRS.
However, SRS is not always feasible or efficient when the population has distinct subgroups, as important characteristics might not be represented accurately. This is where other sampling techniques, like stratified sampling, come into play.
Subgroups
Subgroups, also known as strata in statistics, are divisions within a population that share common attributes. Subgroups are crucial in stratified sampling, where the population is divided based on these shared characteristics before sampling occurs.
For example, in the engineer scenario, dividing engineers into male and female categories creates two subgroups. This division ensures that both male and female perspectives are adequately represented in the sample.
By considering subgroups, researchers can obtain samples that reflect the diversity of the entire population more accurately, thereby leading to more meaningful insights and conclusions.
Probability
Probability is a measure of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). In the context of sampling, probability determines the chance of each member being selected.
In stratified sampling, the probability of selecting someone is typically the same within each subgroup, ensuring consistency across the sample.
For example, in the exercise, each engineer, whether male or female, has a probability of 1 in 10 of being chosen, maintaining fairness in the selection process. Through stratified sampling, the concept of probability helps in ensuring that the sample is both random and representative.
Random Selection
Random selection means choosing participants in such a way that each has an equal opportunity to be included in the sample, without bias or predetermination. It is a cornerstone of effective sampling techniques.
In the case of stratified sampling, random selection is applied within each subgroup, ensuring randomness while respecting the predefined strata.
  • It maintains the objectivity of the sampling process.
  • It reduces the risk of bias and ensures a more accurate representation of the population.
In the given exercise, engineers are randomly selected within each gender group. This method provides an unbiased approach while adhering to the stratified sampling structure, which differs from SRS by its organized approach of partitioning the population first.

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

Two essential features of all statistically designed experiments are (a) compare several treatments; use the double-blind method. (b) compare several treatments; use chance to assign subjects to treatments. (c) always have a placebo group; use the double-blind method. (d) use a block design; use chance to assign subjects to treatments. (e) use enough subjects; always have a control group.

According to Louann Brizendine, author of The Female Brain, women say nearly three times as many words per day as men. Skeptical researchers devised a study to test this claim. They used electronic devices to record the talking patterns of 396 university students who volunteered to participate in the study. The device was programmed to record 30 seconds of sound every 12.5 minutes without the carrier's knowledge. According to a published report of the study in Scientific American, "Men showed a slightly wider variability in words uttered.... But in the end, the sexes came out just about even in the daily averages: women at 16,215 words and men at \(15,669 . " 56\) This difference was not statistically significant. What conclusion can we draw from this study? Explain.

Explain the difference between the types of inference than can usually be made from an observational study and an experiment.

A survey of drivers began by randomly sampling all listed residential telephone numbers in the United States. Of 45,956 calls to these numbers, 5029 were completed. The goal of the survey was to estimate how far people drive, on average, per day. \({ }^{15}\) (a) What was the rate of nonresponse for this sample? (b) Explain how nonresponse can lead to bias in this survey. Be sure to give the direction of the bias.

To gather information about the validity of a new standardized test for tenth- grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10 th-grade student in the selected high schools. What kind of sample is this? (a) A simple random sample (b) \(A\) stratified random sample (c) A cluster sanple (d) \(A\) systematic random sample (e) A voluntary response sample
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.