/*! 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 77 Describe an association between ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 77

Describe an association between two variables. Give a confounding variable that may help to account for this association. People with shorter hair tend to be taller.

Short Answer

Expert verified
The observed association is that people with shorter hair tend to be taller - indicating a negative association between hair length and height. A potential confounding variable in this case could be 'gender' - as generally, men tend to have shorter hair and are typically taller.

Step by step solution

01

Understanding the Variables

Analyze the given statement: 'People with shorter hair tend to be taller.' Here, two variables are given - hair length and height. These are the two variables to be analyzed.
02

Describe the Association

Based on the provided statement, the observed association could be described as: as hair length decreases (or the shorter the hair), the height tends to increase (or people tend to be taller). This indicates a negative relationship or association between the two variables - hair length and height.
03

Give a Confounding Variable

A confounding variable is an external factor that might influence the outcome of the study, or 'confound' the results, hence the name. In this case, a potential confounding variable could be 'gender'. In many societies, men, who tend to be taller on average, also tend to have shorter hair. Therefore, the association that people with shorter hair tend to be taller might actually be influenced by this confounding variable - gender.

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.

Confounding Variable
A confounding variable is an unseen factor that can distort the perceived relationship between two variables. It acts like an invisible character in a story, quietly influencing the plot without being the main focus. For example, in the association between hair length and height, gender serves as a confounding variable. This is because gender influences both hair length and height independently.

  • Men generally have shorter hair and are taller on average.
  • Women, tend to have longer hair and can vary in height.
Recognizing a confounding variable is crucial, as it helps avoid inaccurate conclusions. It ensures that the real connections are identified, rather than attributing relationships to direct causes that don't exist. It reminds us that underlying factors must always be considered for a thorough analysis.
Negative Relationship
Negative relationship describes a situation where an increase in one variable tends to be associated with a decrease in another. In simpler terms, as one thing goes up, the other comes down. This is seen in the statement, "People with shorter hair tend to be taller".

In our example:
  • As hair length decreases, height seems to increase.
This inverse relationship can occur for various reasons, often highlighting a complex interaction between the variables. But beware! Causation isn't always implied, as seen with the confounding variable here: gender. Hence, understanding negative relationships requires careful examination to avoid misconceptions.
Two Variables
In statistics, two variables are often examined to identify and describe relationships. Variables are characteristics or properties that can take on different values or categories. In our example, the two variables are hair length and height. By observing these variables, we try to find patterns or associations.

  • Hair length could range from short to long.
  • Height could range from short to tall.
Understanding these two variables helps us pose questions about the observed behaviors. Why might shorter hair associate with greater height? What factors might link these observations? By exploring the variables, we work towards finding meaningful connections and insights.

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

State whether or not the sampling method described produces a random sample from the given population. The population is the approximately 25,000 protein-coding genes in human DNA. Each gene is assigned a number (from 1 to 25,000 ), and computer software is used to randomly select 100 of these numbers yielding a sample of 100 genes.

State whether or not the sampling method described produces a random sample from the given population. The population is all trees in a forest. We walk through the forest and pick out trees that appear to be representative of all the trees in the forest.

On January \(14,2012,\) Andrew Brown of Great Britain set the world record time ( 40 days) for rowing solo across the northern Atlantic Ocean. On March 14 , 2010, Katie Spotz of the United States became the youngest person to ever row solo across the Atlantic when she completed it in 70 days at the age of 22 years old. Table 1.3 shows times for males and females who rowed solo across the Atlantic Ocean in the last few years. \(^{10}\) (a) How many cases are there in this dataset? How many variables are there and what are they? Is each categorical or quantitative? (b) Display the information in Table 1.3 as a dataset with cases as rows and variables as columns. $$ \begin{array}{ll} \hline \text { Male times: } & 40,87,78,106,67 \\ \text { Female times: } & 70,153,81 \\ \hline \end{array} $$

Teaching Ability In a sample survey of professors at the University of Nebraska, \(94 \%\) of them descrihed themselves as "ahove average" teachers. \({ }^{28}\) (a) What is the sample? What is the population? (b) Based on the information provided, can we conclude that the study suffers from sampling bias? (c) Is \(94 \%\) a good estimate for the percentage of above-average teachers at the University of Nebraska? If not, why not?

About \(60 \%\) of a child's growth hormone is secreted during sleep, so it is believed that a lack of sleep in children might stunt growth. \(^{63}\) (a) What is the explanatory variable and what is the response variable in this association? (b) Describe a randomized comparative experiment to test this association. (c) Explain why it is difficult (and unethical) to get objective verification of this possible causal relationship.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

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.