Question

in the focus Problem at the beginning of t h e study was described comparing the chosofod duck neng boxes Group Inting boere well separated from each other and well hidden by bebush There were of group bowe, which the court showed about 27 hatched. Group Il nesting boses were placed in high lelons and grouped closely together. There were toof70 youp boxes, of which the court showed about 276 hatched. (a) Find a point estimate Pe for Pu, the proportion of that hatch in group inest bowcements Cound your newer to the decima ) Pind lower limit confidence interval for P o und your own to three decimal places) upper limit () Pindpoint estimate Ds for P2 - the proportion of that hatching t o placement on your m other ) Find a 95% confidence interval for p (Hound your answers to three decimal places) lower limit (c) Find a 95% confidence interval for p lower limit - (Round your answers to three decimal places) upper Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than or equal to the proportion of eggs hatched from group It nest boxes? Because the interval contains both positive and negative numbers, we can not say that a higher proportion of eggs hatched in well-eparated and well-hidden nesting boxes. We can not make any conclusions using this confidence interval Because the interval contains only positive numbers, we can say that a higher proportion of eggs hatched in well-separated and well-Widden nesting boxes Because the interval contains only negative numbers, we can say that a higher proportion of eggs hatched in highly visible, closely grouped nesting boxes ed about the higher cost of plong and What conclusions about placement of nest boxes can be drawn in the article discussed in the Focus Problem, additional concerns are r maintaining group I nest box placements. Also at issues the cost efficiency per successful wood duck hatch The eggs hatch equally well in both conditions. A greater proportion of wood duck eggs hatch if the eggs are laid in well-separated, well-hidden nesting boxes No conclusion can be made. A greater proportion of wood duck eggs hatch if the eggs are ad in highly visible, closely groupedesting boxes

Answer 1

Sol 278 ~ 0.583. 477 95% confidence interval for P, = P, I 7 * J Px (1-P)/n. 95% z-value = 1.96. 0.583 + (1-96)* 0.583 (1-0-583) 477 95% confidence interval) 0.539, 0. 6277) lower limit = 0.539 . upper limit = 0.628 P = 12 276 0.354 780 95% contidence interval - P t for ? */ P. * (1-P) 951 Z-critical value = 1.96. 0-354 *(1-0.354) 0.354 I (1-96) * 780 95% confidence interval = 0.320, 0.388] lower limit - 0.320. upper limit = 0.388

(0) 95% contidence interval for P = 0.583, P = 0.354. P, P2 (P, -P₂ ) + P + (1-P) P*(1-P2) 95% critical a-value = 1.96 (0.583-0.354) + (1.96) * 10:58 3 (1-0.583) (0-354*(1-0.354) V 477 780. 95% confidence interval for P, P₂ ir (0.173, 0.285) lower limit = 0.173 upper limit = 0.285 Option c interval contains only positive numbers --- because option B (d) A greater proportion of wood duck eggs hatch if eggs are laid in well-separted well-hidden nesting boxes.