Question

In the papered Hantering dinner belforruvens..(W, 2005),cologist Crow White and the question whether ravons actually towards way from the sound of the years to com counted the number of ravens he could seen shot his gun domis, and counted against are below Before 1.1.4.10 5901252 Alter: 40,7338.2.14.473 Let be the tree number of ravens before the gunshot and p is the true mean number of ravens her the gunshot We want to Click for Ust) HOM 2 g Na Click for Ust) The totis Number Enter your 2 decimal places This would come from a Click for List • Sortion were true The Pos Number Enter your answer correcto del cos So we conclude that There is no evidence for Ho that is, there is no evidence that there is no one in raven before and after gunshots There is strong evidence for Mother, there is strong evidence that there is no difference in avon before and after gunshots There is no evidence again on there is no evidence that there are more revens gunshots There is strong evidence against other is wrong evidence that there we more vers after shots

Answer 1

Solection: Here Weave is of (xii, say) given that number of cavens, before gunshot is of sample size, n, - 12. ; i = IC 12 and numbers of ravens (xaj, say) after gunshot sample size, no = 12, p=1C1)12. Based on the problem, sample mean number of before geenshot', , ZXsi T(+1+4+1+0+5 +2 +0+1+2+5+2) 9 ravens ni i 2 and similarly, X2 nz 3-67. ni 1 2x+(4+0+2+3+3+6+2+3+4+4+2+3) sample variance before gunshot, s = 2(%-žo)? → (1,-1)-61 = 2 xji 2 2 - 34 - 12 similarly, (n-1) să- 2 xaj - ny Xz? 52.3732 (ii Let the mean rrumber of ravens before geenshot Hy : mean number of ravens after gunshot (a) he roant to test, Ha: there are more davens Ho: there is no difference in ravens before and after geenshot: against after grenshots equivalently Ho: Pi= fue against Ha Hi<M2 or, Ho H-M2=against Ha: Po-Hz< 0 homoseedastie (6) To form the test statistie; we assume normale ormality of the data and note that, variance and mean both are unknown. We know, Z (1 -X2) - (M-H2) N(o,) 67 62 + 12 but. 61 62 are unknocon, assume oi?= 63 = 6? (say)

independently and (0-1) 8 Xal (2,-1)-87 + (12-1) 59² Since, Xotno-2 (reproductive prop. E [ (n.) Toy (ns) :] On - 2 (n-1) si + (n-1) 2² 62 E ca ntno-2 { [01-16 -)6P+(12-1):3} is an unbiased estimator of nitha-2 Note that, (x - X 2) - (Hi-H2) ~ N(0,1) Vi independently and (nith-2) ² 62 xnithat (x,-X2) kenee render Hoofiafle ; t = ~ tngth₂-2 can be considered as test statistic. observed t (x1 - xe) {(11-1)81+(12-1834. rendes Ho; ni nith2-2 nz (2-3.67) - 2.06 (Ans.) (34+52.3732) 12+12-2 (*++) a - 22 Р HO (e) The statistie would come from t-distribution with dof = (01+02-2) if Ho cere true (d) p-value [ + < -2-06] where the t22 0.026.< =0.05 Suppose level of significance, * 20.05, So, we conclude that, we rejeet Ho at K = 0.05 ie there is stoong evidence against Ho ie, there is strong evidence that there are more ravels affer gunshots.