Question

!!!!!!!!!!!Please explain in detail how you find the answers!!!!!!!!!!!

3. As a further measure for the effectiveness of the medical program, FAU decides to administer the same test to five students in their first year, and then again when they graduate the program: Use the scores below to conduct a t-test and determine whether the scores significantly change over time.

First Year      Graduation

85    88

88    93

82    86

92    95

91    96

3B. State the t-statistic and cutoff score (.05-test, 2-tailed) in the t-distribution

3C. Was the test significant?

Answer 1

paired t test

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
85	88	-3	1.000
88	93	-5	1.000
82	86	-4	0.000
92	95	-3	1.000
91	96	-5	1.000

b)

mean of difference ,    D̅ =ΣDi / n =   -4.000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    1.000                  
                          
std error , SE = Sd / √n =    1.0000   / √   5   =   0.4472      
                          
t-statistic = (D̅ - µd)/SE = (   -4   -   0   ) /    0.4472   =   -8.9443
                          
Degree of freedom, DF=   n - 1 =    4  

α=0.05
t-critical value , t* =    ±   2.7764   [excel function: =t.inv.2t(α,df) ]               
                          
c)

Decision: test stat < -2.7764  , Reject null hypothesis                      
yes, test was significant