stats

Each of the 5 steps is worth the following point values: Step 1 (8 points), Step 2 (2 points), Step 3 (5 points), Step 4 (5 points), and Step 5 (5 points).

1. The warden of a state correctional institution is concerned about the stress levels of the correctional officers. Specifically, he wants to see if work related stress decreases based upon years of experience on the job. Random samples of officers who have worked at the institution for more than ten years and officers who have worked 10 years or less were administered a scale designed specifically to measure stress among correctional workers. The scale is scored on a 1 to 4 scale (the higher the number, the greater the stress). The results are contained in the data file, “CO Stress.” Test the hypothesis that the officers that there is no difference in stress between those who have been there more than 10 years and the officers who have been there 10 years or less.

Step 1.

H0: µ1 = µ2

H1: µ1 ≠ µ2

Step 2.

α = .05

Step 3.

Independent Samples T-test, Non-directional

Step 4.

Group Statistics

Independent Samples Test

Step 5.

This is not statistically significant because p=.218. T (40) = -1.251, p > .05.

Therefore we fail to reject H0

2. A study is being done on the change in anxiety that occurs throughout a graduate statistics class. A group of 20 students were administered an anxiety score before the first lesson of their class and right after the last unit. Higher scores indicate greater anxiety. Using the data below, test the hypothesis that there is no difference in anxiety scores.

Step 1.

H0: µ1 = µ2

H1: µ1 ≠ µ2

Step 2.

α = .05

Step 3.

Dependent or Paired Samples T-test, Non Directional

Step 4.

Paired Samples Statistics

Paired Samples Test

Step 5.

t(19) = -2.695, p = .014, p < .05. We reject H0. There was a difference in anxiety between the first lesson and the second lesson.

3. A research project was conducted on the relationships between stereotypes and sentencing of offenders convicted of a terrorist act. Subjects in this study read a scenario describing the arrest and conviction of a man who was found to have bomb making materials and was planning a suicide bombing in a large, suburban shopping mall. Subjects one of three versions of the case in which the perpetrator was described as either: African American, Caucasian or Middle Eastern. (a) Test the hypothesis that there is no difference in the sentence administered to all three types of offenders and display the means in a bar graph. (b) If there is a significant difference for sentence, indicate where the significant differences were for each of the three groups. (c) Determine the effect size for offender ethnicity. (d) Based on all of these results, would you make any recommendations to the Justice Department about investigating bias in sentencing? Why or why not? (5)

Step 1.

Ho: µ1 = µ2 = µ3

H1: µ1 ≠ µ2 ≠ µ3

Step 2.

α = .05

Step 3.

ANOVA

Step 4.

Descriptives

Sentence

ANOVA

Sentence

Step 5.

F (2, 57) =4.238, p=.019. p < .05, Therefore, we reject the null hypothesis because the data is statistically significant, showing that there is a difference.

Multiple Comparisons

Dependent Variable: Sentence

Tukey HSD

* The mean difference is significant at the .05 level.

There is a statistical significance between African Americans & Middle Eastern as well as between Caucasians and Middle Easterners.

η2= 17.733/136.983 = .13

This is not a very strong statistic. We can say that 13% of the variation in sentences was based on race.

Mean:

African American = 5.1500, Caucasian = 5.2500, Middle Eastern = 4.0500

__

I would not recommend that the Justice Department open an investigation. The results showed that both Caucasian and African American suspects received larger sentences than Middle Eastern suspects. Moreover, these findings, although significant, were very weak.

MiddleEasternCaucasianAfricanAmerican

Race

5.00

4.00

3.00

2.00

1.00

0.00

Mean Sentence

Sentences based on Race