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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 378trees in tropical rain forests. The least-squares regression line for the transformed data is lny∧=-2.00+2.42lnx∧lny^=-2.00+2.42lnx^

Use this model to estimate the biomass of a tropical tree 30cm in diameter.

Short Answer

Expert verified

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

Step by step solution

01

Given Information

Given data:

02

Explanation

Substituting the value of x:

lny=-2.00+2.42lnx

=-2.00+2.42ln30

=6.23090

Using the exponential formula:

y=10logy

=106.23090

=508.213

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Most popular questions from this chapter

After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

μG=true mean reduction in blood pressureusing the generic drug μG=true mean reduction in blood pressureusing the name@brand drug

μG=true mean reduction in blood pressure

using the generic drug

μG=true mean reduction in blood pressure

using the name@brand drug

In the context of this situation, which of the following describes a Type I error?

a. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.

Which of the following is a categorical variable?

a. The weight of an automobile

b. The time required to complete the Olympic marathon

c. The fuel efficiency (in miles per gallon) of a hybrid car

d. The brand of shampoo purchased by shoppers in a grocery store

e. The closing price of a particular stock on the New York Stock Exchange

T12.2 Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results. The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following transformations would be reasonable for them to try?

I. Plot the square root of the number of Cheerios against diameter.
II. Plot the cube of the number of Cheerios against diameter.
III. Plot the log of the number of Cheerios against the log of the diameter.
IV. Plot the number of Cheerios against the log of the diameter.

a. I and II
b. I and III
c. II and III
d. II and IV
e. I and IV

In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a "fat tax" on sugared soda. Thirtyone percent said that they were in favor of such a tax and 66% were opposed. But when asked if they would support such a tax if the money raised were used to fund health care given the high incidence of obesity in the United States, 48% said that they were in favor and 49% were opposed.
(a) In this situation, explain how bias may have been introduced based on the way the questions were worded and suggest a way that the questions could have been worded differently in order to avoid this bias.
(b) In this situation, explain how bias may have been introduced based on the way the sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.
(c) This poll was conducted only in New York State. Suppose the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on sugared soda were available for each state as well as an overall estimate for the nation as a whole. Identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

The cell that contributes most to the chi-square statistic is

a. men who developed a rash.

b. men who did not develop a rash.

c. women who developed a rash.

d. women who did not develop a rash.

e. both (a) and (d).
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