There has always been a rivalry between the Marines and the

There has always been a rivalry between the Marines and the Army. A study was conducted between a random sample of the two groups to determine if there was a difference in upper body strength based on the number of dead hang pull-ups. The Marines are group 1 and the Army is group 2. Use a two sample independent t test to check the level of significance at 0.05 for the two groups. Show all work for partial credit.

Marines (1)                                        Army (2)  

15                                                           18

20                                                           18

18                                                           14

14                                                           12

20                                                           20

11                                                           9

17

Solution

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 =    16.42857143          
X2 =    15.16666667          
              
Calculating the standard deviations of each group,              
              
s1 =    3.309438163          
s2 =    4.215052392          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    7          
n2 = sample size of group 2 =    6          
Thus, df = n1 + n2 - 2 =    11          
Also, sD =    2.127377955          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    0.593173751          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.20098516      
              
As |t| < 2.200, then we fail to reject Ho.
              
Also, using p values,              
              
p =    0.5650614          
              
As P > 0.05, we fail to reject Ho.

Thus, there is no significant evidence between the mean number of dead hang pull-ups between the two groups. [CONCLUSION]