Question

After conducting a statistical analysis of responses to a survey, Professor Patterson finds a correlation of +2.36 between participation in sporting events and physical injuries. This finding indicates that:

a) There is a strong positive relationship between sporting events and physical injuries.
b) There is no relationship between sporting events and physical injuries.
c) There is a negative relationship between sporting events and physical injuries.
d) The data is invalid and needs further analysis.

Answer 1

The correlation of +2.36 is invalid since correlation coefficients should be within the -1 to +1 range. The data must be re-analyzed to determine the correct correlation between sporting events and physical injuries. The correct answer is d) The data is invalid and needs further analysis.

Step-by-step explanation:

Professor Patterson's finding of a correlation of +2.36 between participation in sporting events and physical injuries is an indication that the data is invalid and needs further analysis.

In statistics, a correlation coefficient must fall between -1 and +1. Values outside this range, such as +2.36, are not possible for a Pearson correlation coefficient. A positive correlation would mean that as participation in sporting events increases, so does the number of physical injuries.

An example of a positive correlation is the relationship between an individual's height and weight. A negative correlation indicates an inverse relationship where one variable increases while the other decreases. For instance, as the magnitude of earthquakes increases, their frequency decreases.

However, the cited value of +2.36 suggests either a misunderstanding of the correlation coefficient's interpretation or an error in calculation.