Question

ID of Respondent	# of Friends who Bully	Respondent was a Bully Victim (0 = No; 1 = Yes)	Gender (0 = Female; 1 = Male)	# of Times Respondent Bullied Others
1	2	1	1	5
2	4	1	0	2
3	3	0	1	8
4	2	0	0	4
5	6	1	1	6
6	3	0	0	2
7	7	1	1	7
8	4	0	0	0
9	2	1	1	1
10	7	1	1	8

1.         What is the proportion of males who bullied others? What is the proportion of females who bullied others? Which gender (male or female) possessed a deeper involvement in bullying others?

2.         Test the hypothesis (at the .05 level of significance) that individuals who were bullied are more likely to bully others. Test the hypothesis (at the .05 level of significance) that individuals who were bullied committed more bullying than those who were not bullied.

3.         Draw a scatter plot of “number of friends who bully” [x axis] and “number of times respondent bullied others” [y axis]. Based only on the scatter plot, do you believe the correlation between these two variables is positive or negative. Why?

4.         If you were to draw one individual from this sample of 10 individuals, what would do characteristics do you believe would be the most likely to be drawn (1 = Bully Victim and Bully Offender; 2 = Bully Victim but not Bully Offender; 3 = Bully Offender but not Bully Victim; or 4 = Non Bully Victim and Non Bully Offender)? Why?

5.         If the researcher used all of these variables to predict whether a respondent was a Bully, which variable (# of friends who bully, respondent was a bully victim, or gender) do you believe would be the strongest predictor? Why?

Answer 1

1.         What is the proportion of males who bullied others? What is the proportion of females who bullied others? Which gender (male or female) possessed a deeper involvement in bullying others?

The total number of males = 6

The total number of females = 4

What is the proportion of males who bullied others?

The proportion of males who bullied others = 6/6 = 1

What is the proportion of females who bullied others?

The proportion of females who bullied others = 3/4 = 0.75

Which gender (male or female) possessed a deeper involvement in bullying others?

From the above answers, we can say that male possessed a deeper involvement in bullying others.

2.         Test the hypothesis (at the .05 level of significance) that individuals who were bullied are more likely to bully others. Test the hypothesis (at the .05 level of significance) that individuals who were bullied committed more bullying than those who were not bullied.

We have to use a Two-Sample t-test for Equal Means to check whether individuals who were bullied are more likely to bully others.

Let us assume:

µ₁ = individuals who were bullied

µ₂ = individuals who were bullied and bully others

The hypothesis of testing is:

The null hypothesis, H₀: µ₁ = µ₂

Individuals who were bullied are equally likely to bully others.

The alternative hypothesis, H₀: µ₁ > µ₂

Individuals who were bullied are more likely to bully others.

From the given output, we have:

Individuals who were bullied = 6

Individuals who were bullied and bully others = 9

Therefore, at a 0.05 significance level, we can say that individuals who were bullied are more likely to bully others.

3.         Draw a scatter plot of “number of friends who bully” [x axis] and “number of times respondent bullied others” [y axis]. Based only on the scatter plot, do you believe the correlation between these two variables is positive or negative. Why?

We are given with:

Number of Friends who Bully	Number of Times Respondent Bullied Others
2	5
4	2
3	8
2	4
6	6
3	2
7	7
4	0
2	1
7	8

The scatter plot is as follows:

The correlation between these two variables is positive because the scatter plot is having an upward trendline.

4.         If you were to draw one individual from this sample of 10 individuals, what would do characteristics do you believe would be the most likely to be drawn (1 = Bully Victim and Bully Offender; 2 = Bully Victim but not Bully Offender; 3 = Bully Offender but not Bully Victim; or 4 = Non Bully Victim and Non Bully Offender)? Why?

If I were to draw one individual from this sample of 10 individuals, 1 = Bully Victim and Bully Offender would be the most likely to be drawn because an individual who was a Bully Victim has a history of Bullying others more.

5.         If the researcher used all of these variables to predict whether a respondent was a Bully, which variable (# of friends who bully, respondent was a bully victim, or gender) do you believe would be the strongest predictor? Why?

If the researcher used all of these variables to predict whether a respondent was a Bully, Gender would be the strongest predictor because most of the males are Bully Victim.