To test the effect of a physical fitness course on ones phys

To test the effect of a physical fitness course on one\'s physical ability, the number of sit-ups that a person could do in 1 minute, both before and after the course, was recorded. Ten randomly selected participants scored as shown in the following table. Can you conclude that a significant amount of improvement took place? Use = 0.01 and assume normality.

(a) Find t. (Give your answer correct to two decimal places.)_______

(ii) Find the p-value. (Give your answer correct to three decimal places.)________

(b) State the appropriate conclusion.

Solution

Let ud = u2 - u1.          
Formulating the null and alternative hypotheses,          
          
Ho:   ud   <=   0
Ha:   ud   >   0
At level of significance =    0.01      
As you can see, this is a    1   tailed test.  
          
Calculating the standard deviation of the differences (third column):          
          
s =    4.270050741      
          
Thus, the standard error of the difference is sD = s/sqrt(n):          
          
sD =    1.350308607      
          
Calculating the mean of the differences (third column):          
          
XD =    4.7      
          
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then  
          
t =    3.480685805 [PART A]

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As df = n - 1 =    9      
          
Then the critical value of t is          
          
tcrit =    2.821437925      
          
Thus, comparing t and tcrit, we   WE REJECT THE NULL HYPOTHESIS.      
          
Also, using p values,          
          
p =    0.003465533 [PART A, II]

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There is a significant amount of improvement on the number of sit-ups per minute. [ANSWER, CONCLUSION, B]