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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 14

Explanation / 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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