Habitats of grizzly bears. Do grizzly bears segregate on the basis of sex? One hypothesis is that female grizzlies avoid male-occupied habitats because of competition for food and cannibalism. A competing theory is that females do not avoid males, but simply have different habitats available to them. These hypotheses were investigated in the Journal of Wildlife Management (July 1995). Grizzly bears were trapped, fitted with a radio collar, and released in the Highwood trapping zone (HTZ) in Alberta, Canada. The percentage of time, y, each bear used the HTZ as a habitat over a four-year period was recorded.

The researchers modeled E(y) as a function of reproductive class at five levels: estrous adult females, adult females with offspring, independent subadult females,

adult males, and independent subadult males. One goal was to compare the mean percentage use of HTZ for the five classes of grizzly bears.

a. Write a model for E(y) that will enable the researchers to carry out the comparison.

b. The sample sizes and sample means for the five classes are shown in the table below. Use this information to find estimates of the b’s in the model you wrote in part a.

c. Give the null hypothesis for a test to determine whether the mean percentage of use of HTZ differs among the grizzly bear classes.

d. The p-value for the test mentioned in part c was reported as .15. Interpret this result.

Grizzly Class n Mean Percentage of Use Estrous adult females 5 38 Adult females with offspring 7 16 Independent subadult females 2 89 Adult males 7 43 Independent subadult males 8 58