13. Four young children were monitored closely over a period of several weeks to measure how much they watched violent television programs and their amount of violent behavior toward their playmates. The results were as follows:
Child’s Code NumberWeekly Viewing of Violent TV (hours)Number of Violent or Aggressive Acts Toward Playmates
G336814 9
R89048 6
C98906 1
L872212 8

Solution:

(a) Make a scatter diagram of the scores;

b. Above Scatter Diagram reflects that there is a strong positive association between Weekly Viewing of Violent TV and their amount of violent behavior toward their playmates. It has high positive correlation co-efficient i.e. as Weekly Viewing of Violent TVincrease, so does their amount of violent behavior toward their playmates

c. The correlation coefficient, r, is equal to 0.923380517between Weekly Viewing of Violent TV and their amount of violent behavior toward their playmates which is calculated using the formula =CORREL() in excel sheet.

d. To test the significance of the correlation we use the t-test and just insert the values of r.

Null Hypothesis: H0:  =  There is no positive association Weekly Viewing of Violent TV and their amount of violent behavior toward their playmates) vs.
Ha:  There is positive association between Weekly Viewing of Violent TV and their amount of violent behavior toward their playmates)
Degre of Freedom= / n-2= / 2
Significant level = / 0.05
(Using with probability value = 0.05 and df= 2)
one-tailed test, critical value of t = / 2.92
Correlation Coefficient / r= / 0.9233

Test-Statistics
3.681
Since 3.6812.92, we can conclude that there is positive association between Weekly Viewing of Violent TV and their amount of violent behavior toward their playmates

e. Co-efficient of determination R2 = (-0.9233)2 = 0.8524

Hence 85.24% percent of the variation in their amount of violent behavior toward their playmatesis accounted by Weekly Viewing of Violent TV. Also, there is positive association between the amount of violent behavior toward their playmatesand the Weekly Viewing of Violent TV.

f. Three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved:

  1. As Weekly Viewing of Violent TVincreases, it affects their amount of violent behavior toward their playmates. It is also reflected by high positive correlation co-efficient of 0.9233 between the amount of violent behavior toward their playmatesand the Weekly Viewing of Violent TV.
  2. High amount of violent behavior toward their playmates is does not promote high level of Weekly Viewing of Violent TVwhich is logical to believe.
  3. There can other variables also be the reason for decrease in violence level as only 85.24% of variation is accounted by the curve of correlation co-efficient between the amount of violent behavior toward their playmatesand the Weekly Viewing of Violent TVwhich can be attributed to the family issues.

14 Five college students were asked about how important a goal it is to them to have a family and about how important a goal it is for them to be highly successful in their work. Each variable was measured on a scale from 0 “Not at all important goal” to 10 “Very important goal.”
StudentFamily GoalWork Goal
A75
B64
C82
D39
E41

Solution:

(a) Make a scatter diagram of the scores;

b. Above Scatter Diagram reflects that there is a weaknegative association between Family Goaland Work Goal. It has smallnegative correlation co-efficient i.e. as Family Goal increases, Work Goal decreases slightly.

c. The correlation coefficient, r, is equal to -0.4490326between Family Goal and Work Goal which is calculated using the formula =CORREL() in excel sheet.

d. To test the significance of the correlation we use the t-test and just insert the values of r.

Null Hypothesis: H0:  =  There is no positive association Family Goal and Work Goal) vs.
Ha:  There is positive association between Family Goal and Work Goal)
Degree of Freedom= / n-2= / 3
Significant level = / 0.05
(Using with probability value = 0.05 and df= 3)
one-tailed test, critical value of t = / 2.353363
Correlation Coefficient / r= / -0.4490326

Test-Statistics
1.938
Since 1.938 < 2.353, we can conclude that there is no positive association between Family Goal and Work Goal.

e. Co-efficient of determination R2 = (-0.4490)2 = 0.2016

Hence 20.16% percent of the variation in family goal is accounted by work goal. Also, there is smallnegative association between thefamily goaland the work goal.

f. Three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved:

  1. As family goal increases, it affects work goal mildly. It is reflected by smallnegative correlation co-efficient of -0.4490 between thefamily goal and the work goal.
  2. Highlevel of family goal does not promote high level of Work Goal which is logical to believe.
  1. There can other variables also be the reason for decrease in family goal as only 20.16% of variation is accounted by the curve of correlation co-efficient between thefamily goal and the work goal which can be attributed to the not readiness for handling family responsibility immediately.