Question

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x	10.9	28.4	24.5	14.3	7.5	27.7	16.2	20.1
y	28	71	39	23	15	30	15	25

(a) Make a scatter diagram of the data.

(b) Use a calculator to verify that Σx = 149.6, Σx² = 3220.10, Σy = 246, Σy² = 9850 and Σxy = 5295.0.

Compute r. (Round to 3 decimal places.)

___________

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

a Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

b Given our value of r, y should tend to decrease as x increases.   

c Given our value of r, y should tend to increase as x increases.

d Given our value of r, y should tend to remain constant as x increases.

Answer 1

Solution :

(a)

X	Y	XY	X^2	Y^2
10.9	28	305.2	118.81	784
28.4	71	2016.4	806.56	5041
24.5	39	955.5	600.25	1521
14.3	23	328.9	204.49	529
7.5	15	112.5	56.25	225
27.7	30	831	767.29	900
16.2	15	243	262.44	225
20.1	25	502.5	404.01	625

n	8
sum(XY)	5295.00
sum(X)	149.60
sum(Y)	246.00
sum(X^2)	3220.10
sum(Y^2)	9850.00
Numerator	5558.40
Denominator	7862.04
r	0.7070
r square	0.4998
Xbar(mean)	18.7000
Ybar(mean)	30.7500
SD(X)	8.3083
SD(Y)	17.9227
b	1.6442
a	0.0037

r = 0.707

c Given our value of r, y should tend to increase as x increases.