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 13.3 31.0 24.5 14.3 7.5 27.7 16.2 20.1 y 24 78 39 23 15 30 15 25 (a) Make a scatter diagram of the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 123456789101112131415161718192021222324252627282930313251015202530354045505560657075 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 154.6, Σx2 = 3432.62, Σy = 249, Σy2 = 10685 and Σxy = 5710.6. 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. Given our value of r, y should tend to remain constant as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases.

Answer 1

Here, we are given 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 13.3 31.0 24.5 14.3 7.5 27.7 16.2 20.1 y 24 78 39 23 15 30 15 25

a) We have to draw a scatter plot. To do so we use MS Excel. The following steps are performed.

1. Enter values of x and y in two cloumns

2. Select insert from the tab and then charts.

3. Select scatter plot and the first option.

4. Click OK

Now to verify the given data we construct the following-

	x	y	x2	y2	xy
	13.3	24	176.8	576	319.2
	31	78	961	6084	2418
	24.5	39	600.25	1521	955.5
	14.3	23	204.49	529	328.9
	7.5	15	56.25	225	112.5
	27.7	30	767.29	900	831
	16.2	15	262.44	225	243
	20.1	25	404.01	625	502.5
	154.6	249	3432.62	10685	5710.6

The formula to calculate r is

= 7189.4/9142.2395

= 0.786

We have to conclude that as x increases whether the value of r implies that y should tend to increase or decrease. Here, from the r value last option is correct that is given our value of r, y should tend to increase as x increases.