Air traffic controllers perform the vital function of regulating the traffic of
ID: 3056564 • Letter: A
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. 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 (a) Complete the F-table. (Round your answers to two decimal places.)
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 48-hour sleep deprivation conditions.There are no significant differences between any of the groups.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 24-hour sleep deprivation conditions.
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 13Explanation / 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. 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 (a) Complete the F-table. (Round your answers to two decimal places.)
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.
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.
We can do one way anova in EXCEL.
steps :
ENTER data into EXCEL sheet --> Data --> Data Analysis --> Anova : Single factor --> Ok --> Input Range : Select all the columns with labels --> Grouped by : Columns --> Labels in first row --> Alpha : 0.05 --> Output Range : select one empty cell --> ok
Test statistic = 4.86
P-value = 0.0236
P-value < alpha
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
Anova: Single Factor SUMMARY Groups Count Sum Average Variance 12 hours 6 137 22.83333 26.96667 24 hours 6 113 18.83333 8.566667 48 hours 6 95 15.83333 10.16667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 148 2 74 4.857768 0.023627 3.68232 Within Groups 228.5 15 15.23333 Total 376.5 17Related Questions
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