Question

Question 1: (20 pts) A university wants to find out whether an Englsh gmogram heligs fheir udets m skills. They design a if the student's soore is hi test to checic for te a) Can the Final Exam

Answer 1

Before	After	d = After - Before
18	22	4
16	17	1
21	25	4
19	16	-3
22	24	2
17	20	3
24	29	5
17	20	3
18	20	2
23	19	-4
16	15	-1
14	15	1
19	26	7
16	18	2
18	18	0
	d-bar =	1.733333333
	s =	2.914659173

Data:     

n = n1 = n2 = 15    

d-bar = 1.733333333    

s (of d) = 2.914659173    

Hypotheses:     

Ho: d-bar ≤ 0    

Ha: d-bar > 0    

Decision Rule:     

α = 0.05    

Degrees of freedom = 15 - 1 = 14

Critical t- score = 1.761310115   

Reject Ho if t > 1.761310115    

Test Statistic:     

SE = s/√n = 2.91465917308321/√15 = 0.752561762   

t = d-bar/SE = 1.73333333333333/0.752561762481463 = 2.303243959   

p- value = 0.0185606    

Decision (in terms of the hypotheses):    

Since 2.303243959 > 1.761 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence to conclude that the program is helpful.