2. A study measuring the fatigue and stress of air traffic controllers resulted

Question

2. A study measuring the fatigue and stress of air traffic controllers resulted in proposals for modification and redesign of the controller's work station. After consideration of several designs for the work station, 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. To answer this question, an experiment was designed that provided measurements of air traffic controller stress under each alternative. To provide the necessary data, the three work station alternatives were installed at the Cleveland Control Center in Oberlin, Ohio. Six controllers were selected at random and assigned to operate each of the systems. A follow-up interview and a medical examination of each controller participating in the study provided a measure of the stress for each controller on each system. Stress was measured on a 0 (no stress) to 20 (very high stress) scale. The data are reported in the table below Controller 1 Controller 2 14 Controller 3 Controller 4 14 Controller 5 16 Controller 6 Stress Level System A System B System C 16 17 13 16 17 16 18 14 15 13 15 13 15 13 Do the sample results justify the conclusion that the population mean stress levels differ for the three systems? That is, are the differences in mean stress levels statistically significant? Use Excel, ? ? ,05, the 5-step procedure discussed in class, and the p-value approach to answer this question. If and only if it is appropriate to do so, determine which pair(s) of treatment means is/are unequal using an experiment-wise Type I error rate of a ,05 for all of the pairwise comparisons. Briefly summarize your findings, in plain English. (4 points)

Explanation / Answer

Excel output:

a)

H0: Population mean stress leves for all systems are equal.

Ha: altleast on mean stress levels of the system is different.

b)

If the p - value is less than 0.05, reject Ho. Or else fail to reject Ho

If test statistic F > 3.68 reject Ho

c)

Test statistic F = 2.11

P - value is 0.1555>0.05

d)

We fail to reject H0

e)

We have enough evidence to support that the means are equal for all the systems

Anova: Single Factor SUMMARY Groups Count Sum Average Variance System A 6 83 13.83333 2.966667 System B 6 95 15.83333 2.166667 System C 6 88 14.66667 3.466667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 12.11111 2 6.055556 2.112403 0.155496 3.68232 Within Groups 43 15 2.866667 Total 55.11111 17

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