Question

Question Help Construct a 90% confidence interval, using the inequality ä- to To<Ha <atte Th 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 3.4 2.4 2.3 2.6 4.8 2.5 4.4 4.1 4.7 4.2 5.1 4.7 1.9 Sleep using the drug 5.8 4.1 4.2 4.4 6.7 3.9 6.6 5.8 7.1 5.5 6.0 6.8 4.5 Calculated for each patient by subtracting the number of hours of sleep with the drug from the number without the drug. The confidence interval is << (Type an integer or a decimal. Round to two decimal places as needed.)

Answer 1

di ² di 2 Let di = x;- Yi Sleep without Sleep using the drug (x) the drug 2 5.76 - 2,4 3.4 S. 8 4,1 -1.7 2,89 2,4 2.3 3.61 -1.9 4,2 4.4 2.6 3,24 -1,8 6.7 -lig 3.61 4.8 2,5 3.9 -1.4 1.96 4.84 4,4 6.6 -2,2 5,8 -1.7 2.89 4.1 7.1 4.7 -2.4 S.16 4.2 s.s -1.3 1.69 S. 6,0 0.81 -0,9 -2.1 4.7 6.8 4.41 4.5 - 2,6 6.76 1.9 Total -24.3 48.23

b-13 d 3 di - 24.3 iz 13 -1.86 S² = LŽ d; 2ū n il 48,23 (3 -(-1,86)² 3.71 3.45 0,26 S = 70,26 0,5° gor. confidence interval fox edis, e al te sa -0.90 <Hp <dt tc Sd rá 1-ac0,90 - d-olo tc = tan = tolo, 12 1. 78 Upper limit corso dttc sd Wh - 1,86 +1.78 x 0, 5) 713 -1.86 + 0,25 -1.61 Lower limit = ă-te sd -1,86 1.78 X0,5 13 -1.86- 0,25 = -2.1]

:. 90% confidence interval for Md is, 2,11 <d -1, 61