Question

A researcher developed a training program designed to improve memory retention. She applied this program to a population of learning-disabled (LD) children in 2^nd grade, where each child received a moderately-intense (MI) and an intense (I) version of the training program for 6 weeks. Afterwards, they were tested with a standardized memory assessment. If she randomly selected Child #5 to compare, which program version produced a better memory score?

Intense			Moderately Intense
Child #	Score		Child #	Score
1	1		1	15
2	6		2	20
3	7		3	19
4	5		4	15
5	8		5	20

Answer 1

Ho :   µd=   0                  
Ha :   µd <   0                  
                          
Level of Significance ,    α =    0.01                  
                          
sample size ,    n =    5                  
                          
mean of sample 1,    x̅1=   5.400                  
                          
mean of sample 2,    x̅2=   17.800                  
                          
mean of difference ,    D̅ =ΣDi / n =   -12.4000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    1.6733                  
                          
std error , SE = Sd / √n =    1.6733   / √   5   =   0.7483      
                          
t-statistic = (D̅ - µd)/SE = (   -12.4   -   0   ) /    0.7483   =   -16.570
                          
Degree of freedom, DF=   n - 1 =    4                  
t-critical value , t* =        -3.7469   [excel function: =t.inv(α,df) ]              
                          
p-value =        0.0000   [excel function: =t.dist(t-stat,df) ]              
Decision:   p-value <α , Reject null hypothesis     

Hence we can conclude that Moderately intense program version produced a better memory score.

  

Please let me know in case of any doubt.

Thanks in advance!

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