9.39 Gunnels. The dataset Gunnels comes from a study on the

habitat preferences of a species of eel, called a gunnel. Biologist

Jake Shorty sampled quadrats along a coastline and recorded a

binary variable, Gunnel, where 1 represents the presence of the

species found in the quadrat and a 0 its absence. Below is output

from a logistic model fit with Time as the explanatory variable,

where Time represents the time of day as "minutes from midnight,"

with a minimum of 383 minutes (about 6:23 a.m.) and a maximum

of 983 minutes (about 1:23 p.m.). The output is given below:

Answer the questions that follow:

a. State the null hypothesis that the P-value of 1.86e-08

allows you to test.

b. What happens to the probability of finding a gunnel as you

get later in the day? Does it get smaller or larger?

c. Find a 95% confidence interval for the slope parameter in

the logistic model.