Question

Intepret all results at the .05 singificance level

2. In order to better prepare for her 8:00am classes, a statistics graduate student designs an experiment to see how various strategies improve test scores. Getting extra sleep and drinking coffee are often said to be good ways to improve focus in class. She assigns half of her participants to 4 hours of sleep the night before a test and the other half to 8 hours. Within these groups, half of the participants are given 50mg of caffeine the morning of the test and the other half are given 100mg of caffeine. She then measures excam performance on a test with scores ranging from 1-15. (50 points) 4 hours of sleep 8 hours of sleep 50mg of caffeine 10 7 12 9 15 7 11 10 12 8 10 9 12 100mg of caffeine 13 11 10 13 11 9 14 15 12 10 11 10 13 A What test should you perform? Be as specific as possible. (5 points) B. Write a sentence describing the main effect of caffeine (include statistical notation). If the main effect was significant, write a second sentence describing which group scored higher/lower. (15 points) C Write a sentence describing the main effect of sleep (include statistical notation. If the main effect was significant, write a second sentence describing which group scored higher/lower. (15 points) D. Write a sentence describing if there was a significant interaction effect or not include statistical notation. Note: you do not need to describe the different groups here./15 points) Bonus: What do these results suggest? Is there an ideal sleep/caffeine combination that appears to be the most effective or particularly ineffective? (2 bonus points)

Answer 1

a)

Repeated measure ANOVA will be used

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b)

Anova: Two-Factor With Replication
SUMMARY	4 hours sleep	8 hours sleep	Total
50mg caffiene
Count	7	7	14
Sum	60	86	146
Average	8.571429	12.28571	10.42857
Variance	1.619048	2.904762	5.802198
100mg caffeine
Count	7	7	14
Sum	79	82	161
Average	11.28571	11.71429	11.5
Variance	4.238095	3.238095	3.5
Total
Count	14	14
Sum	139	168
Average	9.928571	12
Variance	4.686813	2.923077
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	8.035714	1	8.035714	2.678571	0.114755	4.259677
Columns	30.03571	1	30.03571	10.0119	0.004188	4.259677
Interaction	18.89286	1	18.89286	6.297619	0.019242	4.259677
Within	72	24	3
Total	128.9643	27

F stat for caffiene =2.67

p value = 0.11

p avlue > 0.05 , not significant

so, there is no main effect of caffiene

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c)

F stat for hours sleep= 10.012

p value =0.004

p value < 0.05, significant

so, there is main effect of hours of sleep

8 hours sleep have larger score

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d)

F stat for interaction = 6.297

p value = 0.019

p value < 0.05, significant

so, there is an interaction between 2 factors

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