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Chapter 12: Q. AP4.28 (page 832)

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10randomly selected bears. Here is some regression output for these data:

Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth?

a. 20.230±1.695

b. 20.230±3.83

c. 20.230±3.91

d. 20.230±20.22

e. 26.7565±3.83

Short Answer

Expert verified

The correct answer is option (c)

Step by step solution

01

Given information

The given data is

02

Explanation

Park rangers are curious about the weight of the bears that live in their area. The question specifies the output of this data. As a result, it is stated,

c=0.95n=10

The slope estimate is supplied in the output's row "Neck girth" and column "Coef" as follows:

b=20.230

The standard error of the slope is calculated as follows in the row "Neck Girth" and column "SE Coef" of the output:

SEb=1.695

By degrees of freedom, the critical t-value can be identified in the student's T distribution table as,

df=n-2=10-2=8

Then t-values are as follows:

t*=2.306

The confidence interval is calculated as follows:

b±t*×SEb

=20.230±2.306×1.695=20.230±3.91

Option (c) is correct.

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