Question

You worry that individual differences in athletic abilities may be reducing your ability to detect a significant effect of the energy gel on exercise endurance. Therefore, you run the study again using a repeated-measures design. You record the number of minutes n = 4 cyclists could maintain high intensity exercise while consuming only water. A week later, you record the number of minutes the same cyclists could maintain high intensity exercise while consuming water and an energy gel every 20 minutes. Assume you obtain the same data as above: Gel Participan Water t A 84 B 81 с 65 D 58 95 88 74 63 Using all 5 steps of hypothesis testing, at the a = .05 level of significance, perform a two-tailed related samples t test to determine if the number of minutes cyclists could maintain high intensity exercise differed significantly depending on whether they consumed only water or water and the energy gels. 8. Explain why at test for two related samples is the appropriate analysis for this study. (1 point) 9. State the null and alternative hypotheses for a two-tailed test using both words and symbols. (5 points) 10. State the decision criteria for the related samples t test by filling in the blanks in the following statement: I Reject H, ifts or if (.5 points) 11. By hand, calculate the test statistic (t statistic) for this study. Show all steps in your analysis. (1.5 points) 12. What decision should be made regarding the null hypothesis? In your answer, state whether the correct decision is to retain or reject the null hypothesis. Also, provide an interpretation of your findings (i.e., describe what your decision indicates about the difference in number of minutes maintaining high intensity exercise when consuming water versus water and an energy gel). (.5 points)

Answer 1

8)

Because the cyclist are same for both data points

9)

Ho :   µd=   0                  
Ha :   µd ╪   0          

10)

  Level of Significance ,    α =    0.05         

Degree of freedom, DF=   n - 1 =    3                  
t-critical value , t* < - 3.1824 or t > 3.1824 [excel function: =t.inv.2t(α,df) ]    

11)

                          
sample size ,    n =    4                  
                          
mean of sample 1,    x̅1=   72.000                  
                          
mean of sample 2,    x̅2=   80.000                  
                          
mean of difference ,    D̅ =ΣDi / n =   -8.0000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.5820                  
                          
std error , SE = Sd / √n =    2.5820   / √   4   =   1.2910      
                          
t-statistic = (D̅ - µd)/SE = (   -8   -   0   ) /    1.2910   =   -6.197
                          
12)
                          
p-value =        0.0085   [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis     

Conclusion: Number of minutes cyclist meaintain high intensity differe significantly for water and gel

13)

cohen's d = |Dbar/ std dev| =    3.098

Large effect

Please let me know in case of any doubt.

Thanks in advance!

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