a fitness trainer claims that high intensity power training decreases the body f

Question

a fitness trainer claims that high intensity power training decreases the body fat percentages of males. the table shows the body fat percentages of 7 males before and after 10 weeks of high intensity power training. at a(alfa)=0.05

Male 1 2 3 4 5 6 7 Body fat percentage (before) 23.2 22 19 23 21.2 21.8 23.7 Body fate percentage (after) 18.2 22.2 19 19.6 18 17.5 19.6 Alfa=0.05 Claim is? Null Hypothesis is? Alternative Hypothesis is ? This is a Right/Left/two tailed test? The significance level is? The critical value t-critical is? The t-test statistic is? The p-value is? We should Reject /Fail to Reject the Null Hypothesis because? There is sufficient evidence/not sufficient evidence to support the claim that?

Explanation / Answer

The differences are

-5
0.2
0
-3.4
-3.2
-4.3
-4.1

Let ud = u(xafter - xbefore).

a)

Claim: ud < 0 [high intensity power training decreases the body fat percentages of males]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   ud   >=   0  

c)

Ha:   ud   <   0  

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d)

As we can see, this is a    left   tailed test.      
e)
              
At level of significance =    0.05   [ANSWER]      
  
f)

As df = n - 1 =    6          
              
Then the critical value of t is              
              
tcrit =    -   1.943180281   [ANSWER]

  
*****************************

g)
              
Calculating the standard deviation of the differences (third column):              
              
s =    2.120677422          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.801540724          
              
Calculating the mean of the differences (third column):              
              
XD =    -2.828571429          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -3.528917924   [ANSWER, T TEST STATISTIC]

**************************      
              
h)              

Also, using p values,              
              
p =        0.006191973   [ANSWER]

**************************

i)  
              
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.      

***************************
j)

There is sufficient evidence to support the claim that high intensity power training decreases the body fat percentages of males at 0.05 level. [CONCLUSION]  

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