The population (in millions) and the violent crime rate (per 1000) were recorded

Question

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 = 0 in favor of 0 at = .05? (Give your answers correct to three decimal places.)

(A) Calculate r.

answer:___________
(B) Calculate the critical region.
(smaller value):_____________
(larger value):___________

Population 9.6 0.5 3.8 6 0.5 3.6 2.7 0.4 3.3 6.1 Crime Rate 11.5 8.5 7.8 8.9 9.3 7.2 9.4 8.7 7.8 6.7

Explanation / Answer

a)

XY , X2 and Y2 as it was done in the table below.

the sum of every column to get:

X=36.5 , Y=85.8 , XY=323.73 , X2=211.61 , Y2=752.66

r = 0.2937

b) as we have total 10 items

and the alpha = 0.05

therefore the degree of freedom = 10-1 = 9

from the t table

samller value = t<-1.83

bigger value = t>1.83

X Y XY XX YY   9.6 11.5 110.4 92.16 132.25 0.5 8.5 4.25 0.25 72.25 3.8 7.8 29.64 14.44 60.84 6 8.9 53.4 36 79.21 0.5 9.3 4.65 0.25 86.49 3.6 7.2 25.92 12.96 51.84 2.7 9.4 25.38 7.29 88.36 0.4 8.7 3.48 0.16 75.69 3.3 7.8 25.74 10.89 60.84 6.1 6.7 40.87 37.21 44.89

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