Question

A study measuring the fatigue of air traffic controllers resulted in proposals for modficiation and redesign of the controllers' workstation. After consideration of several designs for the workstation, three specific alternatives are selected as having the best potential for reducing controller stress. The key question is: To what extent do the three alternatives differ in terms of their effect on controller stress?

A randomized block design is used to test the hypothesis of no difference in stress levels for the three workstation alternatives. The data for the experiment is located in the Microsoft Excel Online file below. Use ? = 0.01 to test for any significant differences.

Set up the ANOVA table for this problem. Show the entries to 2 decimals, if necessary.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Treatments
Blocks
Error
Total

Calculate the value of the test statistic (to 2 decimals).

Calculate the critical value (to 2 decimals).

Calculate the p-value (to 4 decimals).

	System A	System B	System C
Controller 1	16	15	18
Controller 2	15	15	15
Controller 3	11	12	15
Controller 4	14	12	17
Controller 5	17	13	17
Controller 6	14	13	13

Answer 1

put above data in excel"

Now from data-data analysis: ANOVA two factor without replication:

Source of Variation	SS	df	MS	F	P-value	F crit
treatments	18.78	2	9.39	5.06	0.0303	7.56
Blocks	29.11	5	5.82	3.14	0.0584	5.64
Error	18.56	10	1.86
Total	66.44	17

value of the test statistic =5.06

critical value =7.56

p value =0.0303