Question

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.

2. For a sample of 900 police officers at a local police department, a researcher believes there is a relationship between “number of arrests per month” and “police use of force.” Using the following data, test the null hypothesis at the .01 level of significance that police use of force does not differ by the number of arrests per month that an officer makes. In so doing, identify: (1) the research and null hypothesis, (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.

                                                                 Number Of Arrests Per Month

            Use of Force                           One                  Two                 Three               Four or More               Total

            No Force                                  120                  100                 40                       120                                    380

            Force                                       120                  140                 100                       160                                    520_

                                                            240                  240                 140                       280                                   900

3. How is an Analysis of Variance (ANOVA) similar to and different from a t-test for two samples?

4. What statistical test would a researcher use to test the following research hypothesis: Individuals who report less favorable attitudes toward the police (measured as 1 = very favorable, 2 = somewhat favorable, 3 = somewhat not favorable, and 4 = not at all favorable) are more likely to be sentenced to higher security prisons (measured as 1 = minimum, 2 = medium, and 3 = maximum).

5. Why is it not possible to calculate a chi-square on the following hypothesis: Males have a higher number of total arrests than females?

6. Why is it impossible to calculate a negative F value when using an Analysis of Variance to test a hypothesis?

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Judge 1	5	9	1.8	0.7
Judge 2	5	16	3.2	0.7
Judge 3	5	10	2	3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	5.733333333	2	2.866667	1.954545	0.184168	3.885294
Within Groups	17.6	12	1.466667
Total	23.33333333	14

From the above output

( 1 )

Null hypothesis ( H0 ) :

Alternative hypothesis ( H1 ) : Atleast one mean is different

( 2 )

At alpha = 0.05 L.o.s , df = ( 2,12 )

F critical value = 3.86

( 3 ) Decision :

F cal < F crit

i.e., 1.95 < 3.86

So fail to reject H0

( 4 )

Conclusion :

At = 0.05 L.O.S there is enough evidence to claim that judges do not vary in the sentence lengths imposed on individuals convicted of domestic violence