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 thier 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 list the hypothetical results of this study.

Sleep Deprivation

12 hours 24 hours 48 hours

24 19 17

20 22 22

35 23 23

28 22 14

24 15 17

21 21 16

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

Source of variation SS df MS Fbot

Between groups __ ___ ___ ___

Between persons ___ ____ ____

.w/in group error ____ ____ ____

total ____ ____

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

_ There are no significant differences between any of the group

_There is a significant difference in decision making for the 12 hour and 24 hour sleep deprivation condition

_ There is a significant difference in decision making for the 12 hour and 48 hour sleep deprivation condition

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

Answer 1

using excel data analysis tool for two factor anova, following o/p Is obtained : write data>menu>data>data analysis>anova :two factor without replication>enter required labels>ok, and following o/p Is obtained,

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
subject 1	3	60	20	13.000
subject 2	3	64	21	1.333
subject 3	3	81	27	48.000
subject 4	3	64	21	49.333
subject 5	3	56	19	22.333
	3	58	19	8.333
12 hours	6	152	25	30.267
24 hours	6	122	20	8.667
48 hours	6	109	18	12.567
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	134.94	5	26.9889	2.202	0.1349	3.33
Columns	162.11	2	81.0556	6.614	0.0148	4.10
Error	122.56	10	12.2556
Total	419.61	17

a)

	SS	DF	MS	Fobt
between groups	162.11	2	81.06	6.61
between persons	134.94	5	26.99	2.20
error	122.56	10	12.26
total	419.61	17

b)

The Bonferroni correction sets the significance cut-off at α/n where n is number of comparisons

α/n = 0.05/3 = 0.0167

Numerator d.f.	3
Denominator d.f.	10
MSE	12.26
t-critical value,t(α/2,df)	2.8701

bonferroni critical value=tα/2,df √(MSE(1/ni+1/nj)) = 5.80
confidence interval = mean difference ± critical value          
          
if confidence interval contans zero, then means are not different.          

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	5.00	5.80	-0.80	10.80	means are not different
µ1-µ3	7.17	5.80	1.37	12.97	means are different
µ2-µ3	2.17	5.80	-3.63	7.97	means are not different

so,

_ There is a significant difference in decision making for the 12 hour and 48 hour sleep deprivation condition