Using the following data and a 005 level perform a matched p

Using the following data and a 0.05 level, perform a matched pairs t-test for the mean. Please show all steps/work.

Solution

Let ud = u2 - u1.              

Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0  

At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    7.174766388          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    2.536662983          
              
Calculating the mean of the differences (third column):              
              
XD =    12.375          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.878456492          
              
As df = n - 1 =    7          
              
Then the critical value of t is              
              
tcrit =    +   2.364624252      
              
As t > 2.53666, we   WE REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the quantities in the first column is greater than the quantities in the second column. [CONCLUSION]