Question

A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows: Control Exercise n=10 n = 15 M = 22 M = 16 SS - 120.5 SS = 190.0 has a significant effect. Use an Calculate the t-value and determine whether the alpha level of .05 (hint: this is an independent-me | t= 2.33, reject the null hypothesis, there is a significant effect Ot=4, reject the null hypothesis, there is a significant effect t-1.62, fail to reject the null hypothesis, there is no signficant effect cannot be determined with the information given

Answer 1

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
      
difference in sample means =    x̅1-x̅2 =    22.0000   -   16.0   =   6.000  
                          
pooled std dev , Sp=   √([(SS1 + SS2]/(n1+n2-2)) =    3.6742                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.5000                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   6.0000   -   0   ) /    1.50   =   4.0000
                          
Degree of freedom, DF=   n1+n2-2 =    23                  
p-value =        0.000563   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      

answer: option B)