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 463 eggs in group I boxes, of which a field count showed about 280 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 788 eggs in group II boxes, of which a field count showed about 280 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 99% 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 99% confidence interval for p₂. (Round your answers to three decimal places.)

lower limit
upper limit

(c) Find a 99% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

a)
Total number of sample (n) = 463
number of favourable events (X) = 280

Confidence interval(in %) = 99
z @ 99% = 2.5758


Since we know that

Required confidence interval = (0.6047516198704104-0.0585, 0.6047516198704104+0.0585)
Required confidence interval = (0.546, 0.663)

b)
Total number of sample (n) = 788
number of favourable events (X) = 280

Confidence interval(in %) = 99
z @ 99% = 2.5758

Since we know that

Required confidence interval = (0.3553299492385787-0.0438, 0.3553299492385787+0.0438)
Required confidence interval = (0.312, 0.399)

c)
Total number of sample 1 (n1) = 463
Total number of sample 2 (n2) = 788
number of favourable events (X1) = 280
number of favourable events (X2) = 280

Confidence interval(in %) = 99
z @ 99% = 2.5758

Since we know that