Question

For any mathematical computations, you must show your work to receive full credit.

1. Based on her own experiences in court, a prosecutor believes that some judges provide more severe punishments than other judges for people convicted of domestic violence. Five of the most recent domestic violence sentences (in years) handed down by three judges are recorded below.

Judge 1	Judge 2	Judge 3
1	3	1
1	2	5
3	4	2
2	3	1
2	4	1

Using this information, test the null hypothesis at the .05 level of significance that judges do not vary in the sentence lengths imposed on individuals convicted of domestic violence. In so doing, please: (1) identify the research and null hypotheses, (2) the critical value needed to reject the null, (3) the decision that you made upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

Answer 1

1)

Ho: µ1=µ2=µ3
H1: not all population means are equal

2)F-critical , F(0.05,2,12) = 3.885

3)

ANOVA
	SS	df	MS	F	p-value	F-critical
Between:	5.73	2	2.87	1.955	0.1842	3.885
Within:	17.60	12	1.47
Total:	23.33	14
					α =	0.05

Decision: Fail to reject Ho

(because test stat < 3.885)

4)

conclusion :    there is no enough evidence of significant mean difference among three treatments