Universität Stuttgart Fachbereich Mathematik Mathematische Statistik

Prof. Dr. I. Steinwart
Dipl.-Math. M. Eberts
Dipl.-Math. H. Hang
Universität Stuttgart
Fachbereich Mathematik
Mathematische Statistik
Präsenzblatt 8
4. Juli 2011
Aufgabe P13. Comparison of two sleeping pills
The effect of two sleeping pills A and B needs to be compared. To this end, 10 patients get the
pills A and B in two subsequent nights. This yields the following sleeping durations:
Patient
1
2
A
8
10 7,5
B
6,5
8
3
9
4
5
6
6
7
8,5 9 5,5
8,5
7
6
8
8
9
10
6,5
7
9
7,5 8,5 10
2
Assume that X1 , . . . , X10 , Y1, . . . , Y10 are independent and normally distributed with Xi ∼ N(µX , σX
)
2
(sleeping durations A) and Yi ∼ N(µY , σY ) (sleeping durations B), i = 1, . . . , 10, where the para2
meters µX , µY ∈ R, σX
> 0 and σY2 > 0 are unknown. Determine the 0, 95-confidence intervals for
2
µX − µY and for σX
/σY2 .
1