Question

A school counselor in a high school would like to try out a new conflict-resolution program...

A school counselor in a high school would like to try out a new conflict-resolution program to reduce aggressiveness in students. She first surveyed 16 students using a 20-item instrument to measure their levels of aggression (on a scale of 0 to 10, with higher numbers meaning higher aggression levels). One month after the conflict resolution program was implemented, the students were given the same survey. The data are listed in the table below. The school counselor/researcher has set the significance level at α = .05.

Aggressiveness rating

Subject

Before program

After program

1

6

4

2

2

3

3

3

1

4

5

5

5

7

7

6

4

4

7

2

3

8

4

3

9

2

1

10

8

3

11

3

3

12

5

4

13

5

4

14

8

4

15

6

7

16

1

4

  1. Estimate the standard deviation of the comparison population (that represents the null hypothesis) (2 points total: 1 for work, 1 for answer)
  1. Calculate the standard error (standard deviation of the sampling distribution) (2 points total: 1 for work, 1 for answer)

  1. Calculate the t statistic for the sample (2 points total: 1 for work, 1 for answer)
  1. Because the hypotheses are directional, a one-tailed test can be performed. Determine the critical t value based on the degrees of freedom and the preset alpha level. (1 point)
  1. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” accordingly. (2 points total: 1 for each answer)

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