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The population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan...

The population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan areas. The data are shown in the following table. Do these data provide evidence to reject the null hypothesis that ρ = 0 in favor of ρ ≠ 0 at α = .05? (Give your answers correct to three decimal places.)

Population 9.2 3.9 2.2 6.9 5.4 4.4 4.3 0.5 0.9 3.5
Crime Rate 11.6 7.2 7.6 9.1 6.5 6.9 6.8 9.3 7 8.1

(a) Calculate r.

(ii) Calculate the critical region.
(smaller value)
(larger value)

math   Statistics-And-Probability   
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Answer #1

Solution: Given data1: Number of metiopolion areaA o To reject Nuu hyptheik , P:o and «l 0.05 pulation: | 9.2 39 2.2 6.954 ч.Y 4.3 0.5 0.9 3.5 Cİmevute | ILG 72 구.6 9.1 6.5 69 6. 8 9.3 7081 Nouo uue have to findout- a) Calculate : The formula fo the corelatiơm Coefficient °ổ.γ: Cov(X,y) бу.Ey Ntdeo, we finobut, Xand:v . X 9.2+ 3.942-246.9+5.4+4-y+43+0.5+ 09+35 ะ ul.2 l0 4-10 10 10 に】 t ( ч.ч) (6.9)4(43)(68)-t (65)(93)-(o 9)(1) t (3.5)(81)xiY106 12+28-08+16-12+62.79+35-1+ 30.36+ 29.4 + 46.5+ G.3+ 28.35 ะ |(n2-4.12), (39-4-12)24(2.2-4-12岸(69-4.MH(54-yo5 9-)43y ) (0 5-4 2)+ (09-4122) Nou, 5x l0 a 5.806+0、0484 +3.686壯共구a84 +1.638 +0,048yt 0.0.3&Y 6x + 13, toYYt to .3684十0.3844 10 69.uo lo 5x ะ 6.2401 6x 2.4980 (16-8 ol,(1,2-80β+(46-goi)+A+80ßt (6-5-8 (69-80) 10 12-8881+0、6561+0.168, +11881+2.2801+1,2.3 a 1+1,4641+1 6641 10 lo 056Nao, C0วาelation Coefficient : Cov (X y) 3 10 (2-y^80(t 5022) 300 6 33-0012 3구524 39,016-33.0D, 2 s) Y 3구529 3、152 y x 1,6029 CO 8Yeletion CD-efficient γ し81.6027 (ii) alcutate the c。trca.se gron:- Nloco coe are Andout the criical value Wtth the helpd oritical value caleu lat5 Can caleutate Cveical value here, 心0.05and df:; n-lz)10-1 The critical value 3263 (Prom Ca(cuatata)) eueY CY.ttal value ·g -2.262

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