Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in the table represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter. What conclusion can you reach about the relationship of the diameter of the tree and its height? Height Diameter at breast height Bark thickness 122.0 20 1.1 193.5 36 2.8 166.5 18 2.0 82.0 10 1.2 133.5 21 2.0 156.0 29 1.4 172.5 51 1.8 81.0 11 1.1 148.0 26 2.5 113.0 12 1.5 84.0 13 1.4 164.0 40 2.3 203.3 52 2.0 174.0 30 2.5 159.0 22 3.0 205.0 42 2.6 223.5 45 4.3 195.0 54 4.0 232.5 39 2.2 190.5 36 3.5 100.0 8 1.4

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
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Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in the table represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.

  1. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter.
  2. What conclusion can you reach about the relationship of the diameter of the tree and its height?
Height Diameter at breast height Bark thickness
122.0 20 1.1
193.5 36 2.8
166.5 18 2.0
82.0 10 1.2
133.5 21 2.0
156.0 29 1.4
172.5 51 1.8
81.0 11 1.1
148.0 26 2.5
113.0 12 1.5
84.0 13 1.4
164.0 40 2.3
203.3 52 2.0
174.0 30 2.5
159.0 22 3.0
205.0 42 2.6
223.5 45 4.3
195.0 54 4.0
232.5 39 2.2
190.5 36 3.5
100.0 8 1.4
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