MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The mature eucalyptus trees in a forest vary. It is known what the population of heights of all mature eucalyptuses in the forest is approximately normally distributed. An article in a conversation journal claims that the standard deviation of this population is 9.23 m. You are a researcher who wants to test this claim with a random sample of 42 mature eucalyptuses from the forest. Based on your sample, follow the steps below to construct 90% confidence interval for the population standard deviation of all mature eucalyptus heights in the forest. Then state whether the confidence interval you construct contradicts the article’s claim. (If necessary, consult a list of formulas)
A) illustrated in picture?
B) Based on your sample, graph the 90% confidence interval for the population standard deviation of all mature eucalyptus heights in the forest.Enter the values for the lower and upper limits on the graph to show your confidence interval. Round the values to two decimal places. For the point (♦️) enter the claim 9.23 from the article on your graph.
C) Does the 90% confidence interval you constructed contradict the article’s claim? Choose the best answer Do the confidence interval contradict the claim? Is the claimed standard deviation inside or outside the 90% confidence interval?
Transcribed Image Text:The mature eucalyptus trees in a forest vary. It is known that the population of heights of all mature eucalyptuses in the forest is
approximately normally distributed. An article in a conservation journal claims that the standard deviation of this population is
9.23 m. You are a researcher who wants to test this claim with a random sample of 42 mature eucalyptuses from the forest.
Based on your sample, follow the steps below to construct a 90% confidence interval for the population standard deviation of all
mature eucalyptus heights in the forest. Then state whether the confidence interval you construct contradicts the article's claim. (If
necessary, consult a list of formulas.)
圖
(a)
Click on "Take Sample" to see the results from the random sample.
Number of mature
Sample standard
deviation
Sample mean
Sample variance
Aa
eucalyptuses
Take Sample
42
85.36
6.65
44.2225
To find the confidence interval for the population standard deviation, first find the confidence interval for the population
variance.
Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical
value you need for your 90% confidence interval for the population variance. (Choose the correct critical values from the table
of critical values provided.) When you are done, select "Compute".
Transcribed Image Text:Point estimate of the
population variance:
90% confidence interval for the
Sample size:
population variance:
Critical values
Left critical value:
Left
Right
Xo,995=21.421 X 005=68.053
Right critical value:
90% confidence interval for the
Aa
population standard deviation:
to.975
=25.215 X 025=60.561
Compute
=27.326 X 050=56.942
(b) Based on your sample, graph the 90% confidence interval for the population standard deviation of all mature eucalyptus
heights in the forest.
• Enter the values for the lower and upper limits on the graph to show your confidence interval. Round the values to two
decimal places.
• For the point (•) enter the claim 9.23 from the article on your graph.
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