Chapter PII, Problem 2RE

(a)

To determine

To interpret the y -intercept in this context.

Explanation of Solution

It is given in the question that researchers want to find out are good grades in high school association with family togetherness. It is also given that,

  $\begin{array}{l}n=142\\ \mu =3.78\\ \sigma =2.2\end{array}$

And the equation of the line is as:

  

Thus, from the equation, we can interpret the y -intercept as, students who do not eat with their families have an average GPA of $2.73$ .

(b)

To determine

To interpret the slope in this context.

Explanation of Solution

It is given in the question that researchers want to find out are good grades in high school association with family togetherness. It is also given that,

  $\begin{array}{l}n=142\\ \mu =3.78\\ \sigma =2.2\end{array}$

And the equation of the line is as:

  

Thus, from the equation we can interpret the slope of the equation as that, for each meal a week a student eats with their family, they have a GPA $0.11$ higher than average $2.73$ .

(c)

To determine

To find out what was the mean GPA for these students.

Answer to Problem 2RE

  $3.15$ .

Explanation of Solution

It is given in the question that researchers want to find out are good grades in high school association with family togetherness. It is also given that,

  $\begin{array}{l}n=142\\ \mu =3.78\\ \sigma =2.2\end{array}$

And the equation of the line is as:

  

Thus, the mean GPA for these students in calculated as,

  

(d)

To determine

To explain what did that mean if a student in this study had a negative residual.

Explanation of Solution

It is given in the question that researchers want to find out are good grades in high school association with family togetherness. It is also given that,

  $\begin{array}{l}n=142\\ \mu =3.78\\ \sigma =2.2\end{array}$

And the equation of the line is as:

  

Thus, if a student in this study had a negative residual then this means that he did not follow the model and had lower grades than predicted.

(e)

To determine

To explain do you agree this interpretation.

Answer to Problem 2RE

Yes, we agree.

Explanation of Solution

It is given in the question that researchers want to find out are good grades in high school association with family togetherness. It is also given that,

  $\begin{array}{l}n=142\\ \mu =3.78\\ \sigma =2.2\end{array}$

And the equation of the line is as:

  

The interpretation is that upon hearing of this study, a counsellor recommended that parents who want to improve the grades their children get should get the family to eat together more often. Thus, we agree with this interpretation because there is a positive correlation but there are a lot more factors involved.