Chapter 3.2, Problem 19AYU

Video Games and Grade-Point Average Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week. $h$, to the cumulative grade-point average. $G$, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

(a) Explain why the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable.

(b) Use a graphing utility to draw a scatter diagram.

(c) Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation.

(d) Interpret the slope.

(e) Predict the grade-point average of a student who plays video games for 8 hours each week.

(f) How many hours of video game playing do you think a student plays whose grade-point average is $2.40$?

To determine

To find:

1. Why the number of time spent playing the video game is the independent variable and the cumulative grade point is the dependent variable in the given data.
2. Graph the given data using a graphing utility.
3. Find the line of best fit using a graphing utility and express the model using function notation.
4. Interpret the slope.
5. Predict the grade point average of a student playing video games for 8 hours each week.
6. Find the hours of video game played by a student with grade point average $2.40$.

Answer to Problem 19AYU

Solution:

a. The grade point of a student depends on the time he spends to study. If he is spending more time for playing the video game then his study time is less. Therefore, the grade point of the student depends on the number of hours he plays the video game, whereas his grade point does not affect the number of hours he spends on the game. Therefore, the hours on video game is the independent variable and the grade point is the dependent variable.

b.

c.

d. The slope is negative, $m=-0.0968$. Therefore, we can say that for every one hour the student spends on the video game, he has the possibility of losing $0.0968$ grades.

e. A student spending 8 hours a week for playing video games will possibly get the average grade point as $2.54$.

f. A student with grade point $2.40$ will probably be playing the video game for nearly $9.4$ hours each week.

Explanation of Solution

Given:

The given data is

Formula used:

Calculation:

a. The grade point of a student depends on the time he spends to study. If he is spending more time for playing the video game then his study time is less. Therefore, the grade point of the student depends on the number of hours he plays the video game, whereas his grade point does not affect the number of hours he spends on the game. Therefore, the hours on video game is the independent variable and the grade point is the dependent variable.

b. The graph of the given data is

c. The line of best fit is

The functional notation of the given model is $y=-0.0968x+3.3097$.

d. From the above graph, we can see that the slope is negative, $m=-0.0968$. Therefore, we can say that for every one hour the student spends on the video game, he has the possibility of losing $0.0968$ grades.

e. From the graph, we can see that a student spending 8 hours a week for playing video games will possibly get the average grade point as $2.54$.

f. A student with grade point $2.40$ will probably be playing the video game for nearly $9.4$ hours each week.