Recent research has demonstrated that music-based physical training for elderly

Question

Recent research has demonstrated that music-based physical training for elderly people can improve balance and walking efficiency and reduce the risk of falls (Trombetti et al., 2011). As part of the training, participants walked in time to music and responded to changes in the music's rhythm during a 1-hour per week exercise program. After 6 months, participants in the training group increased their walking speed and their stride length compared to individuals in the control group. The following data are similar to the results obtained in the study. Do the results indicate a significant difference in the stride length for the two groups? Use a two-tailed test with alpha =.05.

Explanation / Answer

Let

u1= mean of exercise group
u2= mean of control group

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  

At level of significance =    0.05          

As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    23          
X2 =    20          
              
Calculating the standard deviations of each group,              
              
s1 =    2.633122354          
s2 =    3.265986324          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    16          
n2 = sample size of group 2 =    16          

Thus, df = n1 + n2 - 2 =    30          

Also, sD =    1.048808848          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.860387768          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.042272456      
                              
Also, using p values,              
              
p =    0.007632564          
              
As |t| > 2.04227, and P < 0.05,    WE REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence at 0.05 level that there is a difference between the stride length for the two groups. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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