Prisons programs such as education programs and therapy groups have many goals, one of which can be to reduce instances of misconduct. One Massachusetts prison is comparing the number of misconduct instances for one year before and after an education program.Make a two-tailed dependent samples t-test at the = 0.05 level using the information below. State your decision on the hypotheses to see if the programming has had a significant effect on inmate misconduct.

Instances of Inmate Misconduct

Inmate

Before Program

After Program

A

5

2

B

15

7

C

7

2

D

3

0

E

5

4

Step 1: State the H₀ and the H₁. (2 points)

H_{0 =}

H_{1 =}

Step 2: Identify the distribution and compute the df. (2 points)

distribution =

df =

Step 3: Identify the critical value of the test statistic and state the decision rule. (2 points)

=

critical value =

decision rule =

Step 4: Compute the obtained value of the test statistic. (9 points)

Instances of Misconduct

Before Program (x₁)

After Program (x₂)

x_D = x₁ - x₂

Inmate A

5

2

Inmate B

15

7

Inmate C

7

2

Inmate D

3

0

Inmate E

5

4

S = 28

Step 5: Make a decision about the null and state the substantive conclusion. (5 points)

It was stated the null would be rejected if the obtained value of the test statistic was greater than ________ or less than ________. The obtained value is ________, which is ________ than ________. Thus, we will ________ the null hypothesis. The conclusion is that: