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

Population	9.6	2	1.9	7.2	0.6	6	5.7	1.9	5.9	3.8
Crime Rate	11	6.5	6.7	7.4	8.3	7.4	8.9	9.4	7.7	7.2

(a) Calculate r.


(ii) Calculate the critical region.
(smaller value)
(larger value)
(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that ρ ≠ 0. Reject the null hypothesis, there is significant evidence that ρ ≠ 0.     Fail to reject the null hypothesis, there is not significant evidence that ρ ≠ 0. Fail to reject the null hypothesis, there is significant evidence that ρ ≠ 0.

Answer 1

a)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.456

ii_)

smaller value = -0.632

larger value = 0.632

b)

Fail to reject the null hypothesis, there is not significant evidence that ρ ≠ 0.