Question

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

Enrollment (thousands)	53	28	27	36	42
Burglaries	86	57	32	131	157

True or false: If the sample data lead us to the conclusion that there is sufficient evidence to support the claim of a linear correlation between enrollment and number of burglaries, then we could also conclude that higher enrollments cause increases in numbers of burglaries.

Short answer

The statement is false.

Step-by-step solution

Given information

The table represents two variables—the number of enrolled students (in thousands) and the burglaries for certain large colleges.

Interpret the correlation

Linear correlation is a measure that describes the significance of linear association between a pair of variables.

The conclusion is that there is sufficient evidence to support the claim of a linear correlation between enrollment and the number of burglaries. It implies there is a significant linear relationship between the populations of the two variables.

It is also known thatcorrelation does not imply causation, which implies that the linear association does not guarantee that one variable causes change in the other.

Thus, the given statement provided is false as a significant association does not imply that higher enrollments cause an increase in the number of burglaries.