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A control group of 8 students were given the same test twice to see whether reta

ID: 3149911 • Letter: A

Question

A control group of 8 students were given the same test twice to see whether retaking the test affected the score. Below are their scores on their first and second attempts. Test the claim that the differences have a mean of zero using a 0.05 significance level. What do the results suggest? Can the null hypothesis be rejected? Yes, because the test statistic does not fall in the critical region. No, because the test statistic falls in the critical region. Yes, because the test statistic falls in the critical region., No, because the test statistic does not fall in the critical region. This suggests that it that the scores are the same after retesting.

Explanation / Answer

Let ud = u2 - u1.              

The differences are

30
70
40
10
30
40
70
70


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 (third column):              
              
s =    28.60387768          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    10.11299794          
              
Calculating the mean of the differences (third column):              
              
XD =    45          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.449719092          
              
As df = n - 1 =    7          
              
Then the critical value of t is              
              
tcrit =    +/-   2.364624252      
              
As |t| > 2.635,   WE REJECT THE NULL HYPOTHESIS.          
              
Hence,

OPTION C: Yes, because the test statistic falls in the critical region. [ANSWER]

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Hence, the score are NOT THE SAME after retesting.

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