Question

Question 1: a) Perform the 9.60 8.75 8.40 9.10 9.25 9.80 10.05 8.15 10.00 9.60 9.80 9.20 9.30 1) sign test, and 11) Wilcoxson signed-rank test to determine if there is any evidence to conclude that the population median exceeds the given hypothesized (or as estimated from the given data) median value. Take a=0.05. b) Construct 80% confidence interval for the population median based on sign test.

Answer 1

Arrange obs in ascending order o nos bople tool 8.15 8.40 8.75 9:10 9.20 9.25 9.30 9.60 10.00 10-05 9.60 9.80 9.80 OSN Here obs. are odd (OPP TOWA .. Median n th 끔 obs 13 22 08- = 6.5 27th obs DO :: medion = 9.30 030 i) for sign test TO n=13. d=0-05 01. Ho: M=9.30 COO- H: M > 9.30 08 Now we give sign to obs. as .observation less than median we will 8 give - Siqn & greater than median we will give + Sign § neglect median 8.45 9.60 8.75 8.40 9.10 9.25 9.80 10.05 8.15 10.00 9.60 9.80 + + + + + 9.20 9.30 O * Test statistic : st (No. of + siqn) = 6 DE Now n'=12 (as we neqlect median) Ky=nika (ka - value from statistical table for sign test) -12-1 (SED 9W eleitola 19 bodo T 01 99 910 noiena. Decision rule : If st > ka then reject Ho Here st. k'a thus we cannot reject Ho at 54.L.O.S. conclusion : population median does not exceed hypothesized median on eur bacie bo to ob nebolo 1 le uomo Value

prilbage du ii) Wilcoxson signed Rank Test Ho: M=9.30 H,: M > 9.30 OL OLE 200 000 X; x; -9.30 Rank 1x; -9.301 Sian (x; -9.30) bbo e doi 9.60 Vib9 We do 0.3 7.5 8.15 -0.55 09 Feb 4 8.410 -0.9 5 Test apie rolli 9.10 -0.2 3 00 TEN 9.25 -0.05 UNH 9.80 UR 10.05 0.5 002 0.75 21:15 8.15 9.5 + OP 29120 sede en + o apie Powo llis quavibem - 19/09 mpa DUE - 11 EURO OSPF O 7.5 10.00 0.7.0.0 ++ 9.60 0.3 7 9.80 0.5 9.8 + 08. 9.20 -0.1 2 9.90 n: 13 ninti) - Tu.n (apie 10.0/) te pilaitote teal bent op en won n =12 Capitolo del boicie moi oulu Test statistic : 1+ (Sum of tve rank) - 57.3 Decision Rule: Reject Ho if I+Tan Where Tain: non- T6.05,12 = 12 (13) (Where T«,n = 14 T005,12=14 from 1919 903 Statistical table) 2941 64 tiba baca blons nibon nowholagog nie02 .. Here T*< To.05.12 . Thus we cannot reject Ho at 6 4.L.O.S. conclusion : Population median does not exceed hypothesised median value. 2

B part :

To construct 80% confidence interval first we check whether the sample is small or large

Criterian to check sample is small or large

if n< 12 the sample is small , otherwise sample is large .

In our case n=13 ,

Therefore Our sample is large .

Now we find ,

$K^{'}+1=\frac{n}{2}-Z_{\frac{\alpha }{2}}*\sqrt{\frac{n}{4}}=\frac{13}{2}-Z_{\frac{0.20}{2}}*\sqrt{\frac{13}{4}}=6.5-1.28*1.8028=4.19\approx 4$

Thereofore ,

K' +1 = 4

Now 80% confidence interval is given by ,

(Value of 4th observation in ascending order ,Value of 4th observation in descending order)

(9.10,9.60)