Question

USE THE 5 STEP METHOD TO ANALYZE THE RESEARCH PROBLEM. MAKE SURE TO SHOW COMPLETE WORK. A researcher tests the question of whether participation in community-sponsored services (such as card games, field trips, etc.) increases the quality of life (as rated from 1 to 10) for older Americans. The research implements the treatment over a 6-month period and then, at the end of the treatment period, measures quality of life in the two groups (each consisting of 50 participants over the age of 80 where one group got the services and one group did not). Here are the results you will need to complete the t-test.

	No Community Services	Community Services
Mean	6.95	7.23
Standard Deviation	1.23	1.55

Answer 1

Ho :   µ1 - µ2 =   0          
Ha :   µ1-µ2 <   0          
                  
Level of Significance ,    α =    0.05          
                  
Sample #1   ---->   no community          
mean of sample 1,    x̅1=   6.95          
standard deviation of sample 1,   s1 =    1.23          
size of sample 1,    n1=   50          
                  
Sample #2   ---->   community         
mean of sample 2,    x̅2=   7.230          
standard deviation of sample 2,   s2 =    1.55          
size of sample 2,    n2=   50          
                  
difference in sample means = x̅1-x̅2 =    6.950   -   7.2300   =   -0.2800
                  
std error , SE =    √(s1²/n1+s2²/n2) =    0.2798          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -0.2800   /   0.2798   ) =   -1.001

p-value =        0.1598 [ excel function: =T.DIST(t stat,df) ]
Conclusion:     p-value>α , Do not reject null hypothesis      
          
There is not enough evidence to conclude that participation in community-sponsored services (such as card games, field trips, etc.) increases the quality of life for older Americans