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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: 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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 7EA
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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.
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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