Question

Sociology/Criminology/Economics: Records comparing unemployment rates, violent crime rates (per 1,000) and property crime rates (per 1,000) were gathered in a state for the years 1975 - 2005 (n = 31). Below are the scatterplots, regression lines, and corresponding statistics for these 31 years.

	Violent Crime -vs- Unemployment x = Unemployment Rate (in %) y = Violent Crime Rate (in crimes per 1,000 people) correlation coefficient: r = 0.049 regression equation: ŷ = 0.061x + 7.12 sample size: n = 31
	Property Crime -vs- Unemployment x = Unemployment Rate (in %) y = Property Crime Rate (in crimes per 1,000 people) correlation coefficient: r = 0.773 regression equation: ŷ = 2.259x + 29.70 sample size: n = 31

Answer the following questions regarding the relationship between unemployment and these two types of crime rates.

(a) Is there a significant linear correlation between unemployment and violent crime rates?

YesNo    

(b) Is there a significant linear correlation between unemployment and property crime rates?

YesNo    

(c) Choose the most valid concluding statement.

There is no correlation between unemployment and crime rates.While there is a significant correlation between unemployment and property crime rates, there is no such correlation between unemployment and violent crime rates.     There is a significant correlation between unemployment and all types of crime rates.

Answer 1

##Using R codes :

##a) No

##b) Yes

##c)

H0 : There is no significant correlation between unemployment & violent crime rates. v/s

H1 :  There is significant correlation between unemployment & violent crime rates.

> r1=0.049;n=31
> t1=r1*sqrt(n-2)/sqrt(1-r1^2);t1
[1] 0.2641904
> ttab=qt(0.975,n-2);ttab
[1] 2.04523

##Since t1 <ttab accept H0 at 5 % l.o.s. Hence no significant correlation

H0 : There is no significant correlation between unemployment & propery crime rates. v/s

H1 :  There is significant correlation between unemployment & property crime rates.

> r2=0.773
> t2=r2*sqrt(n-2)/sqrt(1-r2^2);t2
[1] 6.561622

##Since t2 >ttab reject H0 at 5 % l.o.s. hence significant correlation.

There is no correlation between unemployment and crime rates.While there is a significant correlation between unemployment and property crime rates, there is no such correlation between unemployment and violent crime rates.