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.)

You may need to use the appropriate table in Appendix B to answer this question.

Follow the steps for computing the one-way within-subjects ANOVA (Section 13.4) and post hoc test (Section 13.5).

Sleep Deprivation 12 Hours 24 Hours 48 Hours 22 17 16 17 21 19 32 22 20 25 20 12 21 14 15 20 19 13

Explanation / Answer

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.

Here we have to test the hypothesis that,

H0 : All means are equal.

H1 : Atleast one of the mean is differ than 0.

Assume alpha = level of significance = 0.05

This is the problem of one way ANOVA.

The F-ratio value is 6.9375. The p-value is .012891. The result is significant at p < .05.

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the mean is differ than 0.

Bonferroni p-value:

P i,j unadjusted =[1t(T2 / k1,)]2

and where t() is the cumulative Student's t distribution with its degree of freedom parameter . Note that is the degrees of freedom of error that were established earlier. Also note that the p-value of Bonferroni simultaneous comparison is directly proportional to q, the number of contrasts (pairs) being simultaneously compared.

From this table we can see that :

12 hours and 48 hours are significant.

12 hours and 24 hours are insignificant.

24 hours and 48 hours are insignificant.

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 48-hour sleep deprivation conditions

Summary of Data Treatments 1 2 3 4 5 Total N 6 6 6 18 X 137 113 95 345 Mean 22.8333 18.8333 15.8333 19.167 X2 3263 2171 1555 6989 Std.Dev. 5.1929 2.9269 3.1885 4.7061

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