Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 12: Q.40 (page 814)

Determining tree biomass It is easy to measure the diameter at breast height (in centimeters) of a tree. It’s hard to measure the total aboveground biomass (in kilograms) of a tree because to do this, you must cut and weigh the tree. Biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. The following figure is a scatterplot of the natural logarithm of biomass against the natural logarithm of diameter at breast height (DBH) for $378$ trees in tropical rain forests. The least-squares regression line for the transformed data is ${lny}^{\land} = - 2.00 + 2.42 \ln x^{\land} \hat{\ln y} = - 2.00 + 2.42 \hat{\ln x}$
Use this model to estimate the biomass of a tropical tree $30$ cm in diameter.

Short Answer

Expert verified

$508.213 kg$ is the biomass of a tropical tree $30 cm$ in diameter.

Step by step solution

01

Given Information

Given data:

02

Explanation

Substituting the value of $x$ :

$\ln y = - 2.00 + 2.42 \ln x$

$= - 2.00 + 2.42 \ln 30$

$= 6.23090$

Using the exponential formula:

$y = 10^{\log y}$

$= 10^{6.23090}$

$= 508.213$

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

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$ students was selected from a large high school. For each student, $x = f o o t l e n g t h$ and $y = h e i g h t$ were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Is there convincing evidence that height increases as footlength increases? to answer this question, test the hypothesis

a. $H 0 : β 1 = 0 H_{0} : β_{1} = 0$ versus $H_{α} : β_{1} & g t; 0 . H_{α} : β_{1} > 0$

b. $H 0 : β 1 = 0 H_{0} : β_{1} = 0$ versus $H_{α} : β_{1} < H_{α} : β_{1} & l t; 0$

c $H 0 : β 1 = 0 H_{0} : β_{1} = 0$ versus $H_{α} : β_{1} \neq 0 . H_{α} : β_{1} \neq 0$

d $H_{0} : β_{1} & g t; 0 H_{0} : β_{1} > 0$ versus $H_{α} : β_{1} = 0 . H_{α} : β_{1} = 0$

e. $H 0 : β 1 = 0 H_{0} : β_{1} = 0$ versus $H_{α} : β_{1} & g t; 1 . H_{α} : β_{1} > 1$

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$ students was selected from a large high school. For each student, $x = f o o t l e n g t h$ and $y = h e i g h t$ were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

The slope $β_{1}$ of the population regression line describes

a. the exact increase in height (cm) for students at this high school when foot length increases by $1$ .

b. the average increase in foot length(cm) for students at this high school when height increases by $1$ .

c. the average increase in height (cm) for students at this high school when foot length increases by $1$ .

d. the average increase in foot length (cm) for students in the sample when height increases by $1$

e. the average increase in height(cm) for students in the sample when foot length increases by $1$

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean $4.5$ minutes and standard deviation $0.9$ minutes.

a. Find the probability that Marcella’s shower lasts between $3$ and $6$ minutes on a randomly selected day.

b. If Marcella took a $7$ minute shower, would it be classified as an outlier by the $1.5 I Q R$ rule? Justify your answer.

c. Suppose we choose $10$ days at random and record the length of Marcella’s shower each day. What’s the probability that her shower time is $7$ minutes or greater on at least $2$ of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds $5$ minutes.

Boyle’s law Refers to Exercise 34. We took the logarithm (base $10$ ) of the values for both volume and pressure. Here is some computer output from a linear regression analysis of the transformed data.

a. Based on the output, explain why it would be reasonable to use a power model to describe the relationship between pressure and volume.

b. Give the equation of the least-squares regression line. Be sure to define any variables you use.

c. Use the model from part (b) to predict the pressure in the syringe when the volume is $17$ cubic centimeters.

About $1100$ high school teachers attended a weeklong summer institute for teaching AP Statistics classes. After learning of the survey described in Exercise 56, the teachers in the AP Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted to take a random sample of $100$ teachers at the institute. One of the first decisions the class had to make was what kind of sampling method to use.

a. They knew that a simple random sample was the “preferred” method. With $1100$ teachers in $40$ different sessions, the class decided not to use an SRS. Give at least two reasons why you think they made this decision.

b. The AP Statistics class believed that there might be systematic differences in the proportions of teachers who had tattoos based on the subject areas that they taught. What sampling method would you recommend to account for this possibility? Explain a statistical advantage of this method over an SRS.

See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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