Question

Construct a​ 90% confidence​ interval, using the inequality d overbarminust Subscript c Baseline StartFraction s Subscript d Over StartRoot n EndRoot EndFraction less thanmu Subscript dless thand overbarplust Subscript c Baseline StartFraction s Subscript d Over StartRoot n EndRoot EndFraction . To test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the​ night, researchers randomly select 13 patients and record the number of hours of sleep each gets with and without the new drug.

Patient 1 2 3 4 5 6 7 8 9 10 11 12 13

Sleep without the drug 4.6 4.6 4.9 1.8 2.7 2.1 2.9 2.6 2.7 2.6 4.1 2.1 2.2

Sleep using the drug 6.7 5.3 7.0 4.1 4.1 4.0 4.0 3.9 4.5 4.5 6.3 3.4 3.4

Calculate d for each patient by subtracting the number of hours of sleep with the drug from the number without the drug. The confidence interval is nothingless thanmu Subscript dless than nothing. ​(Type an integer or a decimal. Round to two decimal places as​ needed.)

Answer 1

for 90% CI; and 12 degree of freedom, value of t=			1.782
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		0.247
lower confidence limit                     =		-1.89
upper confidence limit                    =		-1.39

from above 90% CI =(-1.89 ; -1.39)