Mountain pine beetles are small insects that bore into the bark of trees. The female beetles that first infest. the tree emit pheromones to attract other beetles. In response to the pheromones, many beetles bore into the tree and ultimately kill it. The insects can destroy large tree stands within one year. In a study conducted in the Arapaho National Forest in Colorado, researchers from the USDA Forest Service studied the effect of pine beetle outbreaks on the average number of trees in an area. The researchers counted the number of established trees per hectare before a pine beetle outbreak and seven years after an outbreak. The data is listed in the following table: Tree Stand Refore After
Mountain pine beetles are small insects that bore into the bark of trees. The female beetles that first infest. the tree emit pheromones to attract other beetles. In response to the pheromones, many beetles bore into the tree and ultimately kill it. The insects can destroy large tree stands within one year. In a study conducted in the Arapaho National Forest in Colorado, researchers from the USDA Forest Service studied the effect of pine beetle outbreaks on the average number of trees in an area. The researchers counted the number of established trees per hectare before a pine beetle outbreak and seven years after an outbreak. The data is listed in the following table: Tree Stand Refore After
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![Mountain pine beetles are small insects that bore into the bark of trees. The female beetles that first infest
the tree emit pheromones to attract other beetles. In response to the pheromones, many beetles bore into the
tree and ultimately kill it. The insects can destroy large tree stands within one year. In a study conducted in
the Arapaho National Forest in Colorado, researchers from the USDA Forest Service studied the effect of
pine beetle outbreaks on the average number of trees in an area. The researchers counted the number of
established trees per hectare before a pine beetle outbreak and seven years after an outbreak. The data is
listed in the following table:
a.
b.
C.
d.
e.
f.
Tree Stand Before After
984.1
569.9
1136.3 653.3
1
2
3
4
7
8
1139.1 669.6
996.9 573.2
1053.2 629.1
1015.5 575.3
988.8 558.9
1005
569.9
Are the two measurements (before and after the outbreak) independent or dependent? Justify
your answer.
What is the point estimate for the mean difference µd (after minus before)?
What is the standard error for this estimate?
Find the critical value for creating a 95% confidence interval estimating d.
Create the 95% confidence interval in R.
Based on the interval, is there a lower number of trees after the outbreak? Is the difference
significant? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99e37c92-095a-4cae-adf6-01aeaaa5668c%2F1e2689fa-384b-4490-bdb7-3cd1b8c67097%2Fc5fckhk_processed.png&w=3840&q=75)
Transcribed Image Text:Mountain pine beetles are small insects that bore into the bark of trees. The female beetles that first infest
the tree emit pheromones to attract other beetles. In response to the pheromones, many beetles bore into the
tree and ultimately kill it. The insects can destroy large tree stands within one year. In a study conducted in
the Arapaho National Forest in Colorado, researchers from the USDA Forest Service studied the effect of
pine beetle outbreaks on the average number of trees in an area. The researchers counted the number of
established trees per hectare before a pine beetle outbreak and seven years after an outbreak. The data is
listed in the following table:
a.
b.
C.
d.
e.
f.
Tree Stand Before After
984.1
569.9
1136.3 653.3
1
2
3
4
7
8
1139.1 669.6
996.9 573.2
1053.2 629.1
1015.5 575.3
988.8 558.9
1005
569.9
Are the two measurements (before and after the outbreak) independent or dependent? Justify
your answer.
What is the point estimate for the mean difference µd (after minus before)?
What is the standard error for this estimate?
Find the critical value for creating a 95% confidence interval estimating d.
Create the 95% confidence interval in R.
Based on the interval, is there a lower number of trees after the outbreak? Is the difference
significant? Justify your answer.
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