Chapter 3: Q T3.1. (page 200)

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. "The evidence suggests that the association between the number of extracurricular activities a kid participates in and his or her grade point average is close to zero," the guidance counsellor explains.” A correct interpretation of this statement would be that
(a) active students tend to be students with poor grades, and vice versa.
(b) students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa.
(c) students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities.
(d) there is no linear relationship between a number of activities and grade point average for students at this school.
(e) involvement in many extracurricular activities and good grades go hand in hand.

Short Answer

Expert verified

The correct option is (d).

Step by step solution

Given information

The evidence suggests that the association between the number of extracurricular activities a kid participates in and his or her grade point average is close to zero," the guidance counsellor explains.

Concept

The formula used: $y = a + b x$ and $b = r \times \frac{s_{Y}}{s_{X}}$

Calculation

The following is a general definition of a linear relationship between two variables: $y = a + b x$

The linear relationship is predicated on the slope value, $b$ in this case.

It is well knowledge that $b = r \times \frac{s_{Y}}{s_{X}}$

The correlation coefficient is r, and the standard deviations of $X$ and $Y$ are $s_{x}$ and $s_{y}$ respectively. The correlation coefficient is assumed to be zero.

The linear relationship's slope is also $0$ indicating that there is no linear relationship between the two variables. As a result, a correct interpretation of the above statement would be that, due to a correlation coefficient of $0$ there is no linear link between the number of activities and the grade point average for students at this institution. Therefore, Option (d) is the correct interpretation