Question

Related samples t-test:

Test whether semester GPA significantly changes during a semester abroad program. Use a related (dependent) samples t-test and alpha = .05 with a nondirectional test. The data are presented below.

Answer the following questions. You can use SPSS, but if you do this problem “by hand” be sure to show your work.

1.       What are the null & alternative hypotheses?
2.       What are the degrees of freedom?
3.       What is the critical value of t?
4.       What is the observed value of t?
5.       What is your decision about the null hypothesis/why?
6.        If appropriate, calculate Cohen’s d and report its value.
7.       Write the t statistic using appropriate APA style.
8.       How would you interpret your findings?    

          Before program                             During program

                   2.94                                        3.03

                   2.22                                        1.79

                   3.12                                        3.13

                   1.99                                        2.97

                   3.43                                        3.75

                   3.08                                        3.11

                   2.81                                        2.98

                   3.72                                        3.92

                   2.18                                         2.03

                   3.60                                        3.52

Answer 1

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
2.94	3.03	-0.09	0.00
2.22	1.79	0.43	0.30
3.12	3.13	-0.01	0.01
1.99	2.97	-0.98	0.75
3.43	3.75	-0.32	0.04
3.08	3.11	-0.03	0.01
2.81	2.98	-0.17	0.00
3.72	3.92	-0.20	0.01
2.18	2.03	0.15	0.07
3.6	3.52	0.08	0.04

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	29.09	30.23	-1.140	1.225

Ho :   µd=   0                  
Ha :   µd ╪   0                 
                          
Level of Significance ,    α =    0.05       claim:µd=0          
                          
sample size ,    n =    10                  
                          
mean of sample 1,    x̅1=   2.909                  
                          
mean of sample 2,    x̅2=   3.023                  
                          
mean of difference ,    D̅ =ΣDi / n =   -0.114                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    0.3689                  
                          
std error , SE = Sd / √n =    0.3689   / √   10   =   0.1166      
                          
t-statistic = (D̅ - µd)/SE = (   -0.114   -   0   ) /    0.1166   =   -0.977
                          
Degree of freedom, DF=   n - 1 =    9                  
t-critical value , t* =    ±   2.262   [excel function: =t.inv.2t(α,df) ]               
                          
Conclusion:    |test stat | < |critical value |, Do not reject null hypothesis              

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