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.

Sleep Deprivation
12 Hours	24 Hours	48 Hours
21	16	16
17	21	19
33	22	20
25	19	13
22	14	14
20	20	14

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

Source of Variation	SS	df	MS	Fobt
Between groups
Between persons
Within groups (error)
Total

(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 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.

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

Answer 1

a)

ANOVA
Source of Variation	SS	df	MS	F
between groups	149.78	2	74.89	6.71
between persons	131.78	5	26.36	2.36
Error	111.56	10	11.16
Total	393.11	17

b)

Level of significance,α/3 =	0.0167
Numerator d.f.	3
Denominator d.f.	10
MSE	11.16
t-critical value,t(α/2,df)	2.8701

critical value=tα/2,df √(MSE(1/ni+1/nj))=5.53

if absolute difference of means > critical value,means are significnantly different ,otherwise not

population mean difference	critical value			result
µ1-µ2	4.33	5.53			means are not different
µ1-µ3	7.00	5.53			means are different
µ2-µ3	2.67	5.53			means are not different

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