Wolf packs tend to be large extended family groups that have a well-defined hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to size of hunting region? Using radio collars on wolves, the size of the hunting region can be estimated for a given pack of wolves. Let x represent the number of wolves in an extended pack and y represent the size of the hunting region in km2/1000. The following data are representative of one of the national parks. x wolves 23 36 22 64 95 y km2/1000 7.32 12.13 8.12 15.39 16.85 (a) Verify that Σx = 240, Σy = 59.81, Σx2 = 15,430, Σy2 = 787.4283, Σxy = 3369.39, and r ≈ 0.9397. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 1.6756, a ≈ 5.8422, and b ≈ 0.12750. Se a b
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Wolf packs tend to be large extended family groups that have a well-defined hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to size of hunting region? Using radio collars on wolves, the size of the hunting region can be estimated for a given pack of wolves. Let x represent the number of wolves in an extended pack and y represent the size of the hunting region in km2/1000. The following data are representative of one of the national parks.
| x wolves | 23 | 36 | 22 | 64 | 95 |
| y km2/1000 | 7.32 | 12.13 | 8.12 | 15.39 | 16.85 |
| Σx | |
| Σy | |
| Σx2 | |
| Σy2 | |
| Σxy | |
| r |
(b) Use a 1% level of significance to test the claim
| t | |
| critical t |
(c) Verify that
and
| Se | |
| a | |
| b |
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