43-A professor is trying to help students understand that getting better sleep will help with making less errors on their coursework and exams. To test this hypothesis, students were asked how long they slept the night before and given an assessment of 50 items. The number of items incorrect were measured. The professor then suggested they all get additional quality sleep over the next week, then the following week students who did actually sleep better were assessed again and number of errors were counted. There were only 5 students who actually got the recommended additional quality sleep needed so the data below only represent those 5 students since they are the only ones who have "before" and "after" scores. Using the a = .05 significance level, and a two-tailed test, did students with better sleep make significantly less errors than when they were sleep deprived, and if so, how big was the effect (i.e., effect size using the Estimated d proposed by Cohen)?

Mean Number of Letters Remembered

Deprived Sleep	Sufficient Sleep	Diff	Diff-M	(Diff-M)2
9	7
11	8
15	12
10	8
9	9
		MD=		SSD=

Symbols	Values	Notes column ...
MD
SSD
D
df		n-1
S2D		SSD/df; Round to 2 decimal places
SD		Square root of S2D; Round to 2 decimal places
S2MD		S2D /N; Round to 2 decimal places
SMD		Square root of S2MD; Round to 3 decimal places
Obtained t		MD - D / SMD; Round final t-score to 2 decimal places
Critical t		t cutoff using df, a=.05, and two-tailed
Decision (reject null or fail to reject null)		Type answer as "Reject" or "Fail to Reject" (...whichever of those two is correct)
Estimated d value		MD / SD; Round to 2 decimal places
Effect size S, M, or L		Type answer as "Small" or "Medium" or "Large" (...whichever of those three is correct)