Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q T3.6. (page 216)

Which of the following statements is not true of the correlation r between the lengths (in inches) and weights (in pounds) of a sample of brook trout?

a. r must take a value between −1 and 1.

b. r is measured in inches.

c. If longer trout tend to also be heavier, then r > 0.

d. r would not change if we measured the lengths of the trout in centimeters instead of inches.

e. r would not change if we measured the weights of the trout in kilograms instead of pounds.

Short Answer

Expert verified

The correct option is (b) r measured in inches.

Step by step solution

01

Given information

The lengths (in inches) and weights (in pounds) of a sample of brook trout were correlated (r).

02

Explanation

One of the statistical measurements of the strength of the relationship between two variables is the correlation coefficient. It does not have a specific unit. It establishes the boundaries between two numerical values of -1 and 1 It cannot be measured in any unit, including inches, and it has no effect when shifting from one unit to another, such as inches to centimeters and pounds to kilograms.

Hence, the correct option is (b)

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

If women always married men who were 2 years older than themselves, what would be the correlation between the ages of husband and wife?

a. 2

b. 1

c. 0.5

d. 0

e. Can’t tell without seeing the data

Stand mixers The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers.35 The mixer from Walmart (highlighted in red) was much lighter—and cheaper than the other mixers.

a. Describe what influence the highlighted point has on the equation of the least-squares regression line.

b. Describe what influence the highlighted point has on the standard deviation of the residuals and r2

Teenagers and corn yield Identify the explanatory variable and the response variable for the following relationships, if possible. Explain your reasoning.

a. The height and arm span of a sample of 50 teenagers.

b. The yield of corn in bushels per acre and the amount of rain in the growing season.

Putting success How well do professional golfers putt from various distances to the hole? The data show various distances to the hole (in feet) and the percent of putts made at each distance for a sample of golfers.9 Make a scatterplot by hand that shows how the percent of putts made relates to the distance of the putt.

Rushing for points What is the relationship between rushing yards and points scored in the National Football League? The table gives the number of rushing yards and the number of points scored for each of the 16 games played by the Jacksonville Jaguars in a recent season.

a. Make a scatterplot with rushing yards as the explanatory variable. Describe what you see.

b. The number of rushing yards in Game 16 is an outlier in the x-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

c. The number of points scored in Game 13 is an outlier in the y-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.

Sign-up for free