A researcher wants to know whether lack of sleep affects the scores soldiers ach
ID: 2924737 • Letter: A
Question
A researcher wants to know whether lack of sleep affects the scores soldiers achieve in a test of shooting ability. Ten volunteers slept the night before taking the test (S). The other nine were prevented from sleeping for 48 hours prior to the test (NS).
Volunteer
1
2
3
4
5
6
7
8
9
10
Sleep (S) or No Sleep (NS)
S
NS
NS
S
NS
S
NS
NS
NS
S
Test score
25
20
23
14
26
29
20
10
18
22
Volunteer
11
12
13
14
15
16
1
18
19
Sleep (S) or No Sleep (NS)
S
NS
NS
S
S
NS
S
S
S
Test score
20
22
24
18
19
10
28
23
20
Consider the difference between the scores of the two groups.
a) Is this a paired or unpaired situation?
b) Calculate the summary statistics relevant to this problem.
c) Test whether there is evidence of any difference between the scores of the two groups. State clearly the null and alternative hypotheses and show all steps in the hypothesis test.
Volunteer
1
2
3
4
5
6
7
8
9
10
Sleep (S) or No Sleep (NS)
S
NS
NS
S
NS
S
NS
NS
NS
S
Test score
25
20
23
14
26
29
20
10
18
22
Explanation / Answer
(a) No, this is not a paired situation because not every volunteer faced both type of to situation. SLeep or no sleep.
(b) Summary Statistic:
Mean of Test score (For sleep) xsleep= 21.8
Mean of Test score (for no sleep) xnosleep= 19.22
Standard deviation (for sleep) ssleep= 4.614
Standard deviation (for sleep) snosleep= 5.74
Pooled standard deviation sp = sqrt [(n1 -1)s12 + (n2 -1)s22]/(n1 + n2 -2)
= sqrt [(8 * 4.6142 + 7 * 5.742 )/ 15] = 5.17
(c) H0 : No difference between the scores of the two groups.
Ha : THere is significant difference between the scores of the two groups.
test statistic
t = (xsleep - xnosleep)/ sp * sqrt( 1/n1 + 1/n2 )
t = (21.8 - 19.22)/ 5.17 * sqrt(1/9 + 1/8)
t = 2.58 / 2.5121
t = 1.03
Pr(t >1.03) for dF = 15 and alpha = 0.05
tcr = 2.1314
so we can see that t < tcr so we shallnot reject the null hypothesis and can conclude that sleep doesn't affect the test scores.
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