In: Statistics and Probability
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 264 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 808 eggs in group II boxes, of which a field count showed about 268 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 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 |
The proportion of eggs that hatch can be obtained using the formula:
= No. of eggs that hatch / Total no of eggs
Given: In group I, In group II,
(a)
Hence, point estimate for , the proportion of eggs that hatch in group I nest box placements
100(1-)% confidence interval for can be computed using the formula:
Here
From standard normal table,
i.e
= (0.525, 0.615)
95% confidence interval for = (0.525, 0.615)
Lower limit = 0.525
Upper limit = 0.615
Similarly,
(b)
Hence, point estimate for , the proportion of eggs that hatch in group I nest box placements
To obtain the 95% confidence interval for p2,
= (0.299,0.364)
95% confidence interval for = (0.299,.364)
Lower limit = 0.299
Upper limit = 0.364
(c) 100(1-)% confidence interval for difference in proportion can be computed using the formula:
= (0.182,0.294)
95% confidence interval for p1 − p2 = (0.182,0.294)
Lower limit = 0.182
Upper limit = 0.294