Question 869677: On the basis of her experience with clients, a clinical psychologist thinks that
depression may interfere with sleep. She decided to test this idea. The sleep of nine
depressed patients and eight normal controls is monitored for three successive nights.
The average number of hours slept by each subject during the last two nights is shown
Hours of sleep
Depressed 9.2 7.5 3.9 7.1 6.1 6.6 7.4 7.4 5.9
Control 6.7 6.9 9.5 6.8 7.4 8.2 9.2 6.6
Is the clinician correct? Use α = 0.05 in making your decision.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On the basis of her experience with clients, a clinical psychologist thinks that depression may interfere with sleep.
She decided to test this idea.
The sleep of nine depressed patients and eight normal controls is monitored for three successive nights.
The average number of hours slept by each subject during the last two nights is shown.
Hours of sleep
Depressed 9.2 7.5 3.9 7.1 6.1 6.6 7.4 7.4 5.9 ::: mean = 6.82 with s = 1.47
Control 6.7 6.9 9.5 6.8 7.4 8.2 9.2 6.6:: mean = 7.66 with s = 1.16
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Is the clinician correct? Use α = 0.05 in making your decision.
Ho:: ud-uc >= 0
Ha: ud - uc < 0
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sample stat:: ud - uc = 6.82-7.66 = -0.84
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test stat:: t(-0.84) = (-0.84-0)/sqrt[(1.47^2/9)+(1.16^2/8)] = -1.3146
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p-value = P(t < -1.3146 when df = 9+8-2 = 15) = tcdf(-100,-1.3146,15) = 0.1042
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Since the p-value is > 5%, fail to reject Ho.
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Conclusion:: Depression makes no difference in amt. of sleep.
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Cheers,
Stan H.
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