Question

Here are the data from a study in which adolescents were given counseling at the beginning of the school year to see if it had a positive impact on their tolerance for adolescents who were ethnically different from them. Assessments were made right before the treatment and then 6 months later. Did the program work? The outcome variable is scored on an attitude-toward-others test with possible scores ranging from 0 to 50; the higher the score, the more tolerance. Use SPSS or some other computer application to complete this analysis.

Before Treatment	After Treatment
45	46
46	44
32	47
34	42
33	45
21	32
23	36
41	43
27	24
38	41
41	38
47	31
41	22
32	36
22	36
34	27
36	41
19	44
23	32
22	32

Answer 1

Before Treatment	After Treatment	Difference
45	46	-1
46	44	2
32	47	-15
34	42	-8
33	45	-12
21	32	-11
23	36	-13
41	43	-2
27	24	3
38	41	-3
41	38	3
47	31	16
41	22	19
32	36	-4
22	36	-14
34	27	7
36	41	-5
19	44	-25
23	32	-9
22	32	-10

Positive impact on their tolerance mean : before - after < 0

Sample mean of the difference using excel function AVERAGE(), x̅d = -4.1000

Sample standard deviation of the difference using excel function STDEV.S(), sd = 10.5925

Sample size, n = 20

Null and Alternative hypothesis:

Ho : µd ≥ 0

H1 : µd < 0

Test statistic:

t = (x̅d)/(sd/√n) = (-4.1)/(10.5925/√20) = -1.7310

df = n-1 = 19

p-value :

Left tailed p-value = T.DIST(-1.731, 19, 1) = 0.0498

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that counseling had a positive impact on the tolerance for adolescents who were ethnically different from them at 0.05 significance level.