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 21 36 22 68 97 y km2/1000 7.38 12.13 8.18 15.35 16.81 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (b) Use a 1% level of significance to test the claim ρ > 0. (Round your answers to two decimal places.) t = critical t = Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. (c) Find Se, a, and b. (Round your answers to four decimal places.) Se = a = b =

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Description: 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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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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	21	36	22	68	97
y km²/1000	7.38	12.13	8.18	15.35	16.81

(a) Find

Σx,

Σy,

Σx²,

Σy²,

Σxy,

and

(Round r to three decimal places.)

Σx	=
Σy	=
Σx²	=
Σy²	=
Σxy	=
r	=

(b) Use a 1% level of significance to test the claim

ρ > 0.

(Round your answers to two decimal places.)

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

S_e,

and

(Round your answers to four decimal places.)

S_e =
a =
b =

(d) Find the predicted size of the hunting region for an extended pack of 73 wolves. (Round your answer to two decimal places.)
km²/1000

(e) Find an 85% confidence interval for your prediction of part (d). (Round your answers to two decimal places.)

lower limit	km²/1000
upper limit	km²/1000

(f) Use a 1% level of significance to test the claim that

β > 0.

(Round your answers to two decimal places.)

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

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