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 493 eggs in group I boxes, of which a field count showed about 264 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 786 eggs in group II boxes, of which a field count showed about 270 hatched.

(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 90% 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 90% confidence interval for p₂. (Round your answers to three decimal places.)

lower limit
upper limit

(c) Find a 90% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

a)

sample success x =		264
sample size          n=		493
point estimate =sample proportion p̂ =x/n=		0.535

std error se= √(p*(1-p)/n) =		0.0225
for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.0369
lower bound=p̂ -E                       =		0.498
Upper bound=p̂ +E                     =		0.572

b)

point estimate =sample proportion p̂ =x/n=

0.3440

for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.0279
lower bound=p̂ -E                       =		0.316
Upper bound=p̂ +E                     =		0.372

c)

estimated difference in proportion   =p̂1-p̂2   =			0.1910
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0281
for 90 % CI value of z=		1.645
margin of error E=z*std error =		0.046
lower bound=(p̂1-p̂2)-E=		0.145 (please try 0.146 if this comes wrong)
Upper bound=(p̂1-p̂2)+E=		0.237(please try 0.238 if this comes wrong)