/*! 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 102 Multiple choice: Getting a rando... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 102

Multiple choice: Getting a random sample When we use random numbers to take a simple random sample of 50 students from the 20,000 students at a university, a. It is impossible to get the random number 00000 or \(99999,\) since they are not random sequences. b. If we get 20001 for the first random number, for the second random number, that number is less likely to occur than the other possible five-digit random numbers. c. The draw 12345 is no more or less likely than the draw \(11111 .\) d. Since the sample is random, it is impossible that it will be nonrepresentative, such as having only females in the sample.

Short Answer

Expert verified
Option C is correct.

Step by step solution

01

Analyze Option A

Option A states that it's impossible to get random numbers like 00000 or 99999 because they are not random sequences. In simple random sampling, all numbers within the specified range have an equal probability of being selected, which means these numbers could validly be chosen. This makes option A incorrect.
02

Analyze Option B

Option B claims that if the first random number is 20001, then another number like that is less likely to occur for the next random number. In random sampling, each selection is independent, so the probability of drawing any specific number remains constant regardless of previous draws. Therefore, option B is incorrect.
03

Analyze Option C

Option C suggests that drawing the number 12345 is equally likely as drawing 11111. In random sampling, all sequences of numbers, regardless of their pattern or lack thereof, have the same probability of being drawn if they lie within the valid range. This makes option C correct.
04

Analyze Option D

Option D implies that a random sample can't be nonrepresentative, such as having only females in the sample. While a random sample is designed to be representative, it is possible, though unlikely, for a random sample to be nonrepresentative by chance alone. Hence, option D is incorrect.

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.

Random Sample
A random sample is a subset of individuals chosen from a larger population, where each individual has an equal chance of being selected. Imagine you have a big jar filled with colorful marbles. If each one is as likely to be picked as any other, that's similar to how a random sample works in studies.

When doing random sampling, it's important to make sure no bias is introduced during the process. All individuals in the population must have the same opportunity to be included in the sample. This ensures that the sample is truly random.
  • In a simple random sample of students at a university, each student has an equal chance of being chosen, regardless of their student number.
  • This might mean drawing lots, using a random number generator, or another method to ensure fairness.
Probabilities in Sampling
Probabilities in sampling can be thought of like tossing a fair coin. Every time you toss, there is a 50% chance of landing heads and a 50% chance of landing tails, no matter how many times you flip.

In random sampling, each draw or choice is independent of the others, ensuring every selection is random and has an equal probability. This means that patterns or sequences in numbers, like 11111 or 12345, have the same chance of appearance.
  • This probability holds true even if the number sequence seems odd or unlikely.
  • Independence of events ensures that what happens in one selection does not affect the next.
Sampling Bias
Sampling bias occurs when certain members of a population are more likely to be selected than others. This can lead to skewed results and conclusions that do not accurately reflect the whole population.

Imagine if you only picked red marbles from a jar because they were easier to see. Your final count doesn鈥檛 give a true picture of all the colors available. Similarly, in surveys or tests, if certain groups are overrepresented or underrepresented in the sample, this leads to bias.
  • For example, choosing a sample of students by only interviewing those in the library could bias the results as it might not reflect the views of the whole student body.
  • A truly random sample should minimize the risk of bias by giving every individual an equal chance of being included.

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

Stock market associated with poor mental health An Internet survey of 545 Hong Kong residents suggested that close daily monitoring of volatile financial affairs may not be good for your mental health \((J .\) Social and Clinical Psychology \(2002: 21: 116-128) .\) Subjects who felt that their financial future was out of control had the poorest overall mental health, whereas those who felt in control of their financial future had the best mental health. a. What is the population of interest for this survey? b. Describe why this is an observational study. c. Briefly discuss the potential problems with the sampling method used and how these problems could affect the survey results.

Job market for MBA students A February \(2,2003,\) Atlanta Journal Constitution article about the bleak job market for graduating MBA students described an opinion survey conducted by a graduate student at a major state university. The student polled 1500 executive recruiters, asking their opinions on the industries most likely to hire. He received back questionnaires from 97 recruiters, of whom 54 indicated that health care was the industry most likely to see job growth. a. What is the population for this survey? b. What was the intended sample size? What was the sample size actually observed? What was the percentage of nonresponse? c. Describe two potential sources of bias with this survey.

Poker as a profession? Tony's mother is extremely proud that her son will graduate college in a few months. She expresses concern, however, when Tony tells her that following graduation, he plans to move to Las Vegas to become a professional poker player. He mentions that his friend Nick did so and is now earning more than a million dollars per year. Should Tony's anecdotal evidence about Nick soothe his mother's concern?

Gun control More than \(75 \%\) of Americans answer yes when asked, "Do you favor cracking down against illegal gun sales?" but more than \(75 \%\) say no when asked, "Would you favor a law giving police the power to decide who may own a firearm?" a. Which statistic would someone who opposes gun control prefer to quote? b. Explain what is wrong with the wording of each of these statements.

Baseball under a full moon During a baseball game between the Boston Brouhahas and the Minnesota Meddlers, the broadcaster mentions that the away team has won "13 consecutive meetings between the two teams played on nights with a full moon." a. Is the broadcaster's comment based on observational or experimental data? b. The current game is being played in Boston. Should the Boston Brouhahas be concerned about the recent full moon trend?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.