Question

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 465eggs in group I boxes, of which a field count showed about 272 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 816 eggs in group II boxes, of which a field count showed about 276hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ =  

Find a 95% confidence interval for p₁. (Round your answers to three decimal places.)

lower limit
upper limit

(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ =  

Find a 95% confidence interval for p₂. (Round your answers to three decimal places.)

lower limit
upper limit

(c) Find a 95% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

solution:-
given that

(a)p̂1 = x1/n1 = 272/465
   = 0.585
95% confidence for z is 1.96
confidence interval formula
p1 +/- z * sqrt(p1(1-p1)/n1)
0.585 +/- 1.96 * sqrt(0.585*(1-0.585)/465)
(0.540 , 0.630)
lower limit = 0.540
upper limit = 0.630

(b)p̂2 = x2/n2 = 276/816
   = 0.338
95% confidence for z is 1.96
confidence interval formula
p1 +/- z * sqrt(p1(1-p1)/n1)
0.338 +/- 1.96 * sqrt(0.338*(1-0.338)/816)
(0.306 , 0.370)
lower limit = 0.306
upper limit = 0.370

(c)95% confidence for z is 1.96
confidence interval formula for p1-p2
(p1-p2) +/- z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
(0.585 - 0.338) +/- 1.96 * sqrt((0.585(1-0.585)/465) + (0.338(1-0.338)/816))
0.247 +/- 0.055
(0.192 , 0.302)
lower limit = 0.247
upper limit = 0.302