Question

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^{2}) 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 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 and ?represents the population correlation coefficient.

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

Finally, complete the sentence to state the conclusion of the test.

Source: adapted from Fretwell PT, LaRue MA, Morin P, et al. An
Emperor Penguin Population Estimate: The First Global, Synoptic
Survey of a Species from Space. *PLoS ONE* [Online]
**2012**, *7(4)*, e33751.
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0033751
(accessed August 20, 2016).

Select the null and alternative hypotheses from the list.

?0:?=0 and ?1:?<0

?0:?=0 and ?1:?>0

?0:?=0 and ?1:?≠0

?0:?=0 and ?1:?>0

?0:?=0 and ?1:?≠0

?0:?=0 and ?1:?<0

?=?

df =?

Then, use a ?‑distribution table to make the decision to reject the null hypothesis or fail to reject it based on the significance level of ?=0.01.

The decision is to reject ?0, because the ?‑statistic is more extreme than the ?‑critical value.

The decision is to reject ?0, because the ?‑statistic is not as extreme as the ?‑critical value.

The decision is to fail to reject ?0, because the ?‑statistic is not as extreme as the ?‑critical value.

The decision is to fail to reject ?0, because the ?‑statistic is more extreme than either ?‑critical value.

There is ___________________________evidence at the ?=0.01 level to
conclude that

______________________ and _________________________________are
_____________________

.

sufficient

the current population estimates in the sample

the previous population estimates in the sample

not linearly related

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