Air traffic controllers perform the vital function of regulating the traffic of
ID: 3359907 • 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.
(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 12-hour and 48-hour sleep deprivation conditions.
There is a significant difference in decision making for the 24-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 22 18 17 19 22 21 33 22 21 27 21 13 23 15 15 20 20 14Explanation / Answer
Column1
12 hours
24 hours
48 hours
p1
22
18
17
p2
19
22
21
p3
33
22
21
p4
27
21
13
p5
23
15
15
p6
20
20
14
UsingMs excel perform two-way anova without replication. Data > Data analysis > Two way anova without replication.
Anova: Two-Factor Without Replication
Column1
Column2
Column3
Column4
SUMMARY
Count
Sum
Average
Variance
p1
3
57
19
7
p2
3
62
20.6666667
2.33333333
p3
3
76
25.3333333
44.3333333
p4
3
61
20.3333333
49.3333333
p5
3
53
17.6666667
21.3333333
p6
3
54
18
12
12 hours
6
144
24
27.2
24 hours
6
118
19.6666667
7.46666667
48 hours
6
101
16.8333333
12.1666667
ANOVA
Column1
Column2
Column3
Column4
Column5
Column6
Source of Variation
SS
df
MS
F
P-value
F crit
Rows (persons)
117.833333
5
23.5666667
2.02578797
0.16007713
3.325834529
Columns (groups)
156.333333
2
78.1666667
6.71919771
0.01413711
4.102821015
Error
116.333333
10
11.6333333
Total
390.5
17
To perform Bonferroni procedure, conduct t test for two samples with equal variance.
Data > Data analysis > t test for two sample with equal variance.
For 12-hours and 24 hours:
H0 : There is no significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.
H1: There is a significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.
t-Test: Two-Sample Assuming Equal Variances
12 hours
24 hours
Mean
24
19.6666667
Variance
27.2
7.46666667
Observations
6
6
Pooled Variance
17.3333333
Hypothesized Mean Difference
0
df
10
t Stat
1.80277564
P(T<=t) one-tail
0.0507959
t Critical one-tail
1.8124611
P(T<=t) two-tail
0.1015918
t Critical two-tail
2.22813884
Since the p-value for two tail(0.1015) > 0.05, we accept the null hypothesis and conclude that there is no significant difference in decision making for the 12-hour and 24-hour sleep deprivation conditions.
For 12-hours and 48 hours:
H0 : There is no significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.
H1: There is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.
t-Test: Two-Sample Assuming Equal Variances
12 hours
48 hours
Mean
24
16.8333333
Variance
27.2
12.1666667
Observations
6
6
Pooled Variance
19.6833333
Hypothesized Mean Difference
0
df
10
t Stat
2.7978763
P(T<=t) one-tail
0.00943157
t Critical one-tail
1.8124611
P(T<=t) two-tail
0.01886315
t Critical two-tail
2.22813884
Since the p-value for two tail(0.0094) < 0.05, we reject the null hypothesis and conclude that there is a significant difference in decision making for the 12-hour and 48-hour sleep deprivation conditions.
For 24-hours and 48 hours:
H0 : There is no significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.
H1: There is a significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.
t-Test: Two-Sample Assuming Equal Variances
24 hours
48 hours
Mean
19.6666667
16.8333333
Variance
7.46666667
12.1666667
Observations
6
6
Pooled Variance
9.81666667
Hypothesized Mean Difference
0
df
10
t Stat
1.56630479
P(T<=t) one-tail
0.07417305
t Critical one-tail
1.8124611
P(T<=t) two-tail
0.14834611
t Critical two-tail
2.22813884
Since the p-value for two tail(0.0741) > 0.05, we accept the null hypothesis and conclude that there is no significant difference in decision making for the 24-hour and 48-hour sleep deprivation conditions.
Column1
12 hours
24 hours
48 hours
p1
22
18
17
p2
19
22
21
p3
33
22
21
p4
27
21
13
p5
23
15
15
p6
20
20
14
UsingMs excel perform two-way anova without replication. Data > Data analysis > Two way anova without replication.
Anova: Two-Factor Without Replication
Column1
Column2
Column3
Column4
SUMMARY
Count
Sum
Average
Variance
p1
3
57
19
7
p2
3
62
20.6666667
2.33333333
p3
3
76
25.3333333
44.3333333
p4
3
61
20.3333333
49.3333333
p5
3
53
17.6666667
21.3333333
p6
3
54
18
12
12 hours
6
144
24
27.2
24 hours
6
118
19.6666667
7.46666667
48 hours
6
101
16.8333333
12.1666667
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