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

Sleep Deprivation 12 Hours 24 Hours 48 Hours 23 18 17 19 21 21 33 23 21 26 20 13 22 15 15 20 20 15

Explanation / Answer

(a)

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

there are 3 pair of comparison so the bonferroni procedure the least significant difference is given as

lsd=sqrt(2*mse/r)*t(alpha/3,error df)=sqrt(2*9.66/6)*t(0.05/3,10)=sqrt(2*9.66/6)*2.87=5.15

so difference between 12-hour(17) and 48-hour (23.84) are significant as (23.84-17)=6.84 is more than lsd=15

other differences (23.84-19.5=4.34) and (19.5-17=2.5) are not significant

following information has been generated using ms-excel

ANOVA Source of Variation SS df MS F between person 127.7778 5 25.55556 2.64672 between group 143.4444 2 71.72222 7.428078 within group(error) 96.55556 10 9.655556 Total 367.7778 17

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