Assume that the paired data came from a population that is n

Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level, find d.sd, the t test statistic. and the critical values to test the claim that mu d=0. x 10 11 8 12 12 13 9 16 y 13 10 11 12 9 8 9 13 d = (Round to three decimal places as needed.) sd= (Round to three decimal places as needed.) t = (Round to three decimal places as needed.) T a/2= (Round to three decimal places as needed.)

Solution

PAIRED T TEST          
Let ud = u2 - u1.          
Formulating the null and alternative hypotheses,          
          
Ho:   ud   =   0
Ha:   ud   =/=   0

At level of significance =    0.05      
As you can see, this is a    2   tailed test.  
          
          
Calculating the mean of the differences (third column):          
          
d =    0.6 [ANSWER, ITEM 1]

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Calculating the standard deviation of the differences (third column):          
          
s =    2.547329757      
          
Thus, the standard error of the difference is sD = s/sqrt(n):          
          
sD =    0.805536398   [ANSWER, ITEM 2]

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As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then  
          
t =    0.7448453   [ANSWER, ITEM 3]

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As df = n - 1 =    7      
          
Then the critical value of t is          
          
tcrit =    +/- 2.364624252       [ANSWER, ITEM 4]