/*! 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 14 A statistics student who is curi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 14

A statistics student who is curious about the relationship between the amount of time students spend on social networking sites and their performance at school decides to conduct a survey. Three research strategies for collecting data are described below. In each, name the sampling method proposed and any bias you might expect. (a) He randomly samples 40 students from the study's population, gives them the survey, asks them to fill it out and bring it back the next day. (b) He gives out the survey only to his friends, and makes sure each one of them fills out the Survey. (c) He posts a link to an online survey on his Facebook wall and asks his friends to fill out the survey.

Short Answer

Expert verified
(a) Simple Random Sampling, with potential response bias; (b) Convenience Sampling with selection bias; (c) Voluntary Response Sampling with self-selection bias.

Step by step solution

01

Analyze Sampling Strategy and Bias for Method (a)

This method involves selecting 40 students randomly from the entire population under study. This is known as Simple Random Sampling. Since all students have an equal chance of being selected, there is minimal selection bias. However, response bias may occur if students do not take the survey seriously or forget to return it.
02

Analyze Sampling Strategy and Bias for Method (b)

In this method, the student only surveys his friends, which is an example of Convenience Sampling. This method is subject to selection bias since the sample only includes people in the same social circle, which may not be representative of the broader student population.
03

Analyze Sampling Strategy and Bias for Method (c)

For this method, the student posts a link to the survey on his Facebook wall, encouraging his friends to respond. This is a form of Voluntary Response Sampling. Bias can occur as the sample is self-selecting and only includes individuals connected on social media, who choose to respond, possibly leading to overrepresentation of certain groups or opinions.

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 Sampling
In simple random sampling, every member of the population has an equal chance of being selected for the survey. This method is considered one of the most unbiased ways of sampling. Imagine you are picking a name out of a hat filled with names of everyone in your group. Each name has the same probability of being chosen than any other name. This helps to ensure that the sample is representative of the entire population.
  • This method is advantageous for its fairness because each selection does not affect the next.
  • However, it does not entirely eliminate the possibility of bias. Response bias may still occur if participants do not take the survey seriously or if they forget to return it.

When implemented properly, simple random sampling is a powerful tool for obtaining a sample with minimal selection bias. It is like hitting the "reset" button, providing everyone an equal opportunity to participate.
Convenience Sampling
Convenience sampling involves selecting participants that are easiest to reach, rather than using a randomized process. This method is particularly appealing due to its simplicity and the fact it often requires less time and resources.
  • For example, surveying your friends or classmates because they are readily available is a typical case of convenience sampling.
  • While this might be time-saving, it is highly prone to selection bias.

Selection bias occurs because the sample lacks variety and does not reflect the larger population. Group dynamics, such as similar opinions and behaviors, can skew the results, leading to conclusions that aren't representative of the larger group.
Voluntary Response Sampling
Voluntary response sampling allows participants to decide whether they want to be part of a survey. Usually, a link or invitation is shared widely, and people choose to respond if they wish.
  • This method leverages the willingness of individuals to participate.
  • However, it often results in a self-selected sample, which is less reliable for generalizing findings to the entire population.

Bias can occur because those who decide to respond might share certain characteristics or opinions that differ from non-respondents. For example, people more interested in the survey topic may be more inclined to participate, thereby skewing the data. Thus, the responses may not adequately reflect the opinions of those who chose not to participate.
Selection Bias
Selection bias occurs when the sample collected is not representative of the population intended to be analyzed. This type of bias is evident in methods like convenience sampling and voluntary response sampling.
  • It often arises when individuals are selected in a non-random manner.
  • The sample can end up being skewed towards a particular group, leading to misleading conclusions.

The key to minimizing selection bias lies in ensuring each population member has an equal chance of being included in the sample. Simple random sampling is one way to achieve this, as it randomly selects participants from the entire population.
Response Bias
Response bias happens when the answers given by survey participants are not entirely truthful or accurate, impacting the overall quality of the data collected.
  • This can occur for various reasons, such as a misunderstanding of the question or the respondent's tendency to provide what they perceive as socially acceptable answers.
  • In some cases, participants might rush through the survey, leading to inaccuracies.

One way to minimize response bias is by crafting clear and neutral questions and ensuring that participants understand the survey's purpose. Encouraging honesty and ensuring anonymity can also help reduce this type of bias, leading to more reliable and authentic data.

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

Exercise and mental health. A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to ensure representative proportions of \(18-30,31-40\) and \(41-55\) year olds from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results. (a) What type of study is this? (b) What are the treatment and control groups in this study? (c) Does this study make use of blocking? If so, what is the blocking variable? (d) Does this study make use of blinding? (e) Comment on whether or not the results of the study can be used to establish a causal relationship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large. (f) Suppose you are given the task of determining if this proposed study should get funding. Would you have any reservations about the study proposal?

In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 74 points with a standard deviation of 8.9 points. The student who took the make-up the following day scored 64 points on the exam. (a) Does the new student's score increase or decrease the average score? (b) What is the new average? (c) Does the new student's score increase or decrease the standard deviation of the scores?

For each part, compare distributions (1) and (2) based on their means and standard deviations. You do not need to calculate these statistics; simply state how the means and the standard deviations compare. Make sure to explain your reasoning. Hint: It may be useful to sketch dot plots of the distributions. A. \((1) 3,5,5,5,8,11,11,11,13 (2) 3,5,5,5,8,11,11,11,20\) (b)\( (1) -20,0,0,0,15,25,30,30 (2) -40,0,0,0,15,25,30,30\) (c) \((1) 0,2,4,6,8,10 (2) 20,22,24,26,28,30\) (d) \((1) 100,200,300,400,500 (2) 0,50,300,550,600\)

A large college class has 160 students. All 160 students attend the lectures together, but the students are divided into 4 groups, each of 40 students, for lab sections administered by different teaching assistants. The professor wants to conduct a survey about how satisfied the students are with the course, and he believes that the lab section a student is in might affect the student's overall satisfaction with the course. (a) What type of study is this? (b) Suggest a sampling strategy for carrying out this study.

In order to assess the effectiveness of taking large doses of vitamin \(\mathrm{C}\) in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were assigned a placebo, and the rest were evenly divided between \(1 \mathrm{~g}\) Vitamin \(\mathrm{C}, 3 \mathrm{~g}\) Vitamin \(\mathrm{C},\) or \(3 \mathrm{~g}\) Vitamin \(\mathrm{C}\) plus additives to be taken at onset of a cold for the following two days. All tablets had identical appearance and packaging. The nurses who handed the prescribed pills to the patients knew which patient received which treatment, but the researchers assessing the patients when they were sick did not. No significant differences were observed in any measure of cold duration or severity between the four medication groups, and the placebo group had the shortest duration of symptoms. \(^{60}\) (a) Was this an experiment or an observational study? Why? (b) What are the explanatory and response variables in this study? (c) Were the patients blinded to their treatment? (d) Was this study double-blind? (e) Participants are ultimately able to choose whether or not to use the pills prescribed to them. We might expect that not all of them will adhere and take their pills. Does this introduce a confounding variable to the study? Explain your reasoning.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.