3 SolutionLet ud u2 u1 Formulating the null and alternativ

Solution

Let ud = u2 - u1.              
Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/ 0 [ANSWER, OPTION A]

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At level of significance =    0.1          
As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    2.424621183          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.699927846          
              
Calculating the mean of the differences (third column):              
              
XD =    1.666666667          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.381197827 [test statistic, ANSWER]
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As df = n - 1 =    11          
              
Then the critical value of t is              
              
tcrit =    +/-   1.795884819 [CRITICAL VALUE, ANSWER]
              
Thus, comparing t and tcrit, we   WE REJECT THE NULL HYPOTHESIS.          
              
So, YES, AS WE REJECT THE NULL HYPOTHESIS. [ANSWER, OPTION D]