Question

In: Statistics and Probability

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

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

Solutions

Expert Solution

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


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