Air traffic controllers perform the vital function of regulating the traffic of

Question

Air traffic controllers perform the vital function of regulating the traffic of passenger planes. Frequently, air traffic controllers work long hours with little sleep. Researchers wanted to test their ability to make basic decisions as they become increasingly sleep deprived. To test their abilities, a sample of 6 air traffic controllers is selected and given a decision-making skills test following 12-hour, 24-hour, and 48-hour sleep deprivation. Higher scores indicate better decision-making skills. The table lists the hypothetical results of this study.

(a) Complete the F-table. (Round your answers to two decimal places.)

(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that apply.)

There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.There are no significant differences between any of the groups.

You may need to use the appropriate table in Appendix B to answer this question.

Sleep Deprivation 12 Hours 24 Hours 48 Hours 21 17 15 17 21 19 33 22 20 25 20 12 21 13 14 19 19 13

Explanation / Answer

Step 1                                      
   Null Hypothesis Ho :           µ1 =µ2 =µ3                       
   Alternative Hypothesis :           µ1 µ2 µ3                       
Step 2                                      
   Degrees of freedom between = k - 1 = 3 - 1 = 2                                  
   Degrees of freedom Within = n - k = 18 - 3 = 15                                  
                                      
   Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.682                                  
                                      
Step 3                                      
   Grand Mean = G / N = 22.667+18.667+15.5 / 3 = 18.945                                  
    SST = ( Xi - GrandMean)^2 = (21-18.945)^2 + (17-18.945)^2 + (33-18.945)^2 + ……..& so on = 424.944                                  
   SS Within = (Xi - Mean of Xi ) ^2 =,(21-22.667)^2 + (17-22.667)^2 + (33-22.667)^2 + ……..& so on = 270.167                                  
                                      
   SS Between = SST - SS Within = 424.944 - 270.167 = 154.777                                  
Step 4                                      
   Mean Square Between = SS Between / df Between = 154.777/2 = 77.389                                  
   Mean Square Within = SS Within / df Within = 270.167/15 = 18.011                                  
                                      
Step 5                                      
   F Cal = MS Between / Ms Within = 77.389/18.011 = 4.297                                  
   We got |F cal| = 4.297 & |F Crit| =3.682                                  
                                      
MAKE DECISION                                      
   Hence Value of |F cal| > |F Crit|and Here We Reject Ho                                  

   There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions

ONE WAY ANOVA Treatments Mean = X /n 12 21 17 33 25 21 19 22.667 24 17 21 22 20 13 19 18.667 48 15 19 20 12 14 13 15.5

Step 1                                      
   Null Hypothesis Ho :           µ1 =µ2 =µ3                       
   Alternative Hypothesis :           µ1 µ2 µ3                       
Step 2                                      
   Degrees of freedom between = k - 1 = 3 - 1 = 2                                  
   Degrees of freedom Within = n - k = 18 - 3 = 15                                  
                                      
   Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.682                                  
                                      
Step 3                                      
   Grand Mean = G / N = 22.667+18.667+15.5 / 3 = 18.945                                  
    SST = ( Xi - GrandMean)^2 = (21-18.945)^2 + (17-18.945)^2 + (33-18.945)^2 + ……..& so on = 424.944                                  
   SS Within = (Xi - Mean of Xi ) ^2 =,(21-22.667)^2 + (17-22.667)^2 + (33-22.667)^2 + ……..& so on = 270.167                                  
                                      
   SS Between = SST - SS Within = 424.944 - 270.167 = 154.777                                  
Step 4                                      
   Mean Square Between = SS Between / df Between = 154.777/2 = 77.389                                  
   Mean Square Within = SS Within / df Within = 270.167/15 = 18.011                                  
                                      
Step 5                                      
   F Cal = MS Between / Ms Within = 77.389/18.011 = 4.297                                  
   We got |F cal| = 4.297 & |F Crit| =3.682                                  
                                      
MAKE DECISION                                      
   Hence Value of |F cal| > |F Crit|and Here We Reject Ho                                  

   There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions

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