To determine how climate change and habitat loss will influence Antarctic species, baseline estimates of population sizes and distributions are needed. To this end, a group of researchers estimated the population sizes of all breeding colonies of emperor penguins (Aptenodytes fosteri) along Antarctic coastlines using satellite imagery (Fretwell et al., 2012). For each breeding colony encountered, the researchers determined the latitude, longitude, and area (m) of the colony, and estimated the total number of emperor penguins present. Then, they compared their colony size estimates to previously published estimates. Suppose the researchers want to determine if there is a linear relationship between the colony latitudes and the current population estimates, so they decide to conduct a two-tailed t-test for no linear relationship. From 44 data points, they calculate the linear regression equation to be ŷ = -21881.15255 – 382.65545x where ŷ is the predicted current population estimate and x is the colony latitude. The standard error of the slope, SE,, is 196.89529. The researchers examine the residuals plot and determine that all of the requirements for using a t-test for no linear relationship have been met. First, determine the null and alternative hypotheses of the test. ß represents the slope of the population regression line and p represents the population correlation coefficient. Next, compute the t-statistic (t) and the degrees of freedom (df). Give your answer for t precise to three decimals. df =
To determine how climate change and habitat loss will influence Antarctic species, baseline estimates of population sizes and distributions are needed. To this end, a group of researchers estimated the population sizes of all breeding colonies of emperor penguins (Aptenodytes fosteri) along Antarctic coastlines using satellite imagery (Fretwell et al., 2012). For each breeding colony encountered, the researchers determined the latitude, longitude, and area (m) of the colony, and estimated the total number of emperor penguins present. Then, they compared their colony size estimates to previously published estimates. Suppose the researchers want to determine if there is a linear relationship between the colony latitudes and the current population estimates, so they decide to conduct a two-tailed t-test for no linear relationship. From 44 data points, they calculate the linear regression equation to be ŷ = -21881.15255 – 382.65545x where ŷ is the predicted current population estimate and x is the colony latitude. The standard error of the slope, SE,, is 196.89529. The researchers examine the residuals plot and determine that all of the requirements for using a t-test for no linear relationship have been met. First, determine the null and alternative hypotheses of the test. ß represents the slope of the population regression line and p represents the population correlation coefficient. Next, compute the t-statistic (t) and the degrees of freedom (df). Give your answer for t precise to three decimals. df =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:To determine how climate change and habitat loss will influence Antarctic species, baseline estimates of population sizes and
distributions are needed. To this end, a group of researchers estimated the population sizes of all breeding colonies of
emperor penguins (Aptenodytes fosteri) along Antarctic coastlines using satellite imagery (Fretwell et al., 2012). For each
breeding colony encountered, the researchers determined the latitude, longitude, and area (m) of the colony, and estimated
the total number of emperor penguins present. Then, they compared their colony size estimates to previously
published estimates.
Suppose the researchers want to determine if there is a linear relationship between the colony latitudes and the current
population estimates, so they decide to conduct a two-tailed t-test for no linear relationship. From 44 data points, they
calculate the linear regression equation to be
ŷ = -21881.15255 – 382.65545x
where ŷ is the predicted current population estimate and x is the colony latitude. The standard error of the slope, SE,, is
196.89529. The researchers examine the residuals plot and determine that all of the requirements for using a t-test for no
linear relationship have been met.
First, determine the null and alternative hypotheses of the test. ß represents the slope of the population regression line and p
represents the population correlation coefficient.
Transcribed Image Text:Next, compute the t-statistic (t) and the degrees of freedom (df). Give your answer for t precise to three decimals.
df =
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