Question

2. Suppose a random group of 8 patients from Question 1 who had ACL injuries were asked to perform the "Y Balance Test”, however this time the patients performed the test once while standing on their injured leg, and then after a 5 minute rest period were asked to perform the test again while standing on their uninjured leg. The results are recorded below: Patient injured leg score uninjured leg score 1 2 3 4 5 6 7 8 86.3 85.1 79.2 83.7 82.6 87.3 88.1 89.5 89.7 86.0 80.4 80.1 82.6 87.0 89.7 92.4 For patients with ACL injuries are average scores on the "Y Balance Test" different while standing on the injured leg versus the uninjured leg? If needed, you may assume that performance on the "Y Balance Test" is normally distributed on both injured and uninjured legs. (a) [2 marks] Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study.

Answer 1

a)

Ho :   µd=   0                  
Ha :   µd ╪   0                  
                          

b)

Level of Significance ,    α =    0.1                  
                          
sample size ,    n =    8                  
                          
mean of sample 1,    x̅1=   85.225                  
                          
mean of sample 2,    x̅2=   85.988                  
                          
mean of difference ,    D̅ =ΣDi / n =   -0.7625                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.1771                  
                          
std error , SE = Sd / √n =    2.1771   / √   8   =   0.7697      
                          
t-statistic = (D̅ - µd)/SE = (   -0.7625   -   0   ) /    0.7697   =   -0.991

c)
                          
Degree of freedom, DF=   n - 1 =    7                  

                          
p-value =        0.3549   [excel function: =t.dist.2t(t-stat,df) ]   

d)

Decision:   p-value>α , Do not reject null hypothesis          

We can conclude that average scores are not different.

Please let me know in case of any doubt.

Thanks in advance!

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