91Ó°ÊÓ

The table representing the number of enrolled students (in thousands) and the number of burglaries for randomly selected large colleges in the recent years is provided.

The value of\(r{\rm{ is }}0.499\).

The P-value is 0.393.

The critical values are \( \pm \) 0.878.

Theformula of t-statistic for the correlation coefficient is stated as follows:

\(t = \frac{r}{{\sqrt {\frac{{1--{r^2}}}{{n--2}}} }}\)

Where

\(r = \frac{{n\left( {\sum {xy} } \right)--\left( {\sum x } \right)\left( {\sum y } \right)}}{{\sqrt {\left( {\left( {n\sum {{x^2}} } \right)--{{\left( {\sum x } \right)}^2}} \right)\left( {\left( {n\sum {{y^2}} } \right)--{{\left( {\sum y } \right)}^2}} \right)} }}\)

As per the formula of the correlation coefficient, the measure will be unaffected if the role of variables is changed.

Resultant of this, the test statistic measure and hence the P-value will be unaltered.

The critical values are obtained from the t-distribution table at n–2 degrees of freedom, which are unaffected by switching the variables.

Thus, if the variable enrolment and burglaries are switched, there will be no change in any of the given values.

Therefore, r, P-values, and critical values won’t change if the variables are switched.