Question

A researcher is evaluating the effectiveness of an anti-truancy program for youth. A sample of at-risk youth were selected to participate in the program, and their number of days truant per month were recorded before they completed the program and then again afterward. The data are below. Use a five-step hypothesis test and an alpha of .05 to test the hypothesis that the program significantly reduced youths' truancy.

Type or neatly write all five steps clearly, with steps labeled and answers circled or highlighted where needed.

	Before	After
Youth	x1	x2
A	2	1
B	3	2
C	1	2
D	0	0
E	5	4
F	4	5
G	9	8
N = 7

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: the program is not significantly reduced youths' truancy.

Alternative hypothesis: H_a: the program significantly reduced youths' truancy.

H₀: µ_d = 0 versus H_a: µ_d > 0

This is a right tailed test.

We take difference as before minus after.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

µ_d = 0

Dbar = 0.2857

S_d = 0.9512

n = 7

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (0.2857 - 0)/[ 0.9512/sqrt(7)]

t = 0.7947

df = n – 1 = 7 - 1 = 6

α = 0.05

The p-value by using t-table is given as below:

P-value = 0.2285

P-value > α

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the program significantly reduced youths' truancy.