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 13.7, 29.4, 24.5, 14.3, 7.5, 27.7, 16.2, 20.1

y 23, 76, 39, 23, 15, 30, 15, 25

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 153.4, Σx² = 3346.78, Σy = 246, Σy² = 10330 and Σxy = 5522.9.

*** 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.

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

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

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

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

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