9 Test of abstract reasoning is given to random sample of st

9) Test of abstract reasoning is given to random sample of students before and after they completed a formallogiccourse.Theresultsaregivenbelow.Atthe0.05significancelevel,test the claim that the mean score is not affected by the course.

Before74837588846393849177 After73777077746795838475

Determinewhetherthesamplesareindependentordependent.questions10to14arepoints each)

Solution

9.

These samples are DEPENDENT, because the same students are involved in each test. Thus, we could match them with each other.

Let

u2 = after scores
u1 = before scores

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    two   tailed test.      
              
Calculating the standard deviation of the differences (difference column)
              
s =    2.064104241          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.461547739          
              
Calculating the mean of the differences (third column):              
              
XD =    -0.05          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -0.108331156          
              
As df = n - 1 =    19          
              
Then the critical value of t is              
              
tcrit =    +/-   2.093024054      
              
As |t| < 2.093, we   WE FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is NO significant evidence that the mean score is affected by the course. [CONCLUSION]