24. 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 (m2) of the colony, and estimated the total number of emperor penguins present. Then, they compared their colony size estimates to previously published estimates.

The researchers want to determine if there is a linear relationship between the previous population estimates and the current population estimates, so they decide to conduct a two-tailed test for no linear relationship. From 29 data points, they calculate the linear regression equation to be

=925.25556+0.71001

where is the predicted current population estimate and is the previous population estimate. The standard error of the slope, SE, is 0.10942. The researchers examine the residuals plot and determine that all of the requirements for using a test for no linear relationship have been met.

First, determine the null and alternative hypotheses of the test.

represents the slope of the population regression line.

Select the null and alternative hypotheses.0:=0 and :<0

0:=0 and :0

0:=0 and :>0

Next, compute the statistic () and the degrees of freedom (df). Give your answer for precise to three decimals.

= ____________________

df = _____________________

Finally, complete the sentence to state the conclusion of the test. ( choose from answer bank)

There is __________________ evidence at the =0.01 level to conclude that________________ and _________________ are

ANSWER BANK:

1. not correlated
2. related
3. correlated
4. not related
5. different
6. all of the previous population estimates
7. not linearly related
8. the previous population estimates in the sample
9. convincing
10. the same
11. all of the current population estimates
12. the current population estimates in the sample
13. linearly related
14. not convincing