Question

Show all work, due 09/07

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

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.

Answer 1

Let us divide the data into two groups.

Group 1 – Respondent was not a bully victim but Bullied Others

Group 2 – Respondent was a bully victim and Bullied Others.

From the data, we calculate Mean and Std Deviation for the two groups:

Group 1

x₁ (Mean) = 3.5

s₁ (Std Dev) = 3.415

n₁ = 4

Group 2

x₂ (Mean) = 4.833

s₂ (Std Dev) = 2.787

n₂ = 6

Null and Alternate Hypothesis

H₀: Mean of Group 2 is same as that of Group 1 (µ₁ = µ₂)

H_a: Mean of Group 2 is greater than that of Group 1 (µ₂ > µ₁)

Alpha = 0.05

Test Statistic

t = (x_{2 ­­}– x₁)/{s₂²/n₂ + s₁²/n₁}^1/2 = 0.650

P-value = TDIST(0.650,4+6-2,1) = 0.267

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis.

Conclusion

There is no difference between the two groups ie Individuals bully irrespective if they were bullied or not.