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 24-hour sleep deprivation conditions.

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

Sleep Deprivation 12 Hours 24 Hours 48 Hours 23 17 17 18 21 20 34 23 21 27 21 13 22 15 15 20 21 15

Explanation / Answer

a) Using Minitab

One-way ANOVA: 12 Hours, 24 Hours, 48 Hours

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 12 Hours, 24 Hours, 48 Hours

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 156.3 78.17 4.51 0.029
Error 15 260.2 17.34
Total 17 416.5

Here P value < alpha 0.05 for Hours, we reject H0h

Thus we conclude that there is significance difference among the means of 12hours, 24 hours and 48 hours

and P value < alpha 0.05 for Person, we reject H0p.

Thus we conclude that there is significance difference among the means of persons

b) Correct answer: Option (B)

Bonferroni correction simply divides the experimental-wise error rate by the number of orthogonal contrasts.

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