Question

You have created a new short-cut method that you hope will enable students to learn more material

in the same amount of time when compared with the usual (old) teaching method. Of course, the

method may actually slow down students’ ability to learn. You test this new method by comparing the

performances of identical twins using each of these methods. Using can you conclude that

there is a difference between the methods?

H0:

H1:

=

Decision Rule:

The results of the tests are:

Old New

Pair Method Method Test:

A 87 75

B 63 61

C 55 51

D 92 82

E 44 42

F 78 55

Conclusion

the alfa level we are using is 0.05

the alfa level we are using is 0.05

Answer 1

Ho :   µd=   0
Ha :   µd ╪ 0

Degree of freedom, DF=   n - 1 =    5  
t-critical value , t* =        2.571 [excel function: =t.inv.2t(α,df) ]
decision rule: reject Ho, if t > 2.571

paired t test-

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
87	75	12	10.028
63	61	2	46.694
55	51	4	23.361
92	82	10	1.361
44	42	2	46.694
78	55	23	200.694

mean of difference ,    D̅ =ΣDi / n =   8.833                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    8.110                  
                          
std error , SE = Sd / √n =    8.1097   / √   6   =   3.3108      
                          
t-statistic = (D̅ - µd)/SE = ( 8.83 -   0   ) /    3.3108   =   2.6681

decision: reject Ho, because t =2.6681 >2.571

conclusion: there is enough evidence to conlcude that there is a difference between the methods