Question

Determine the point estimate of the population​ proportion, the margin of error for the following confidence​ interval, and the number of individuals in the sample with the specified​ characteristic, x, for the sample size provided. Lower bound = 0.593​, Upper bound = 0.867, n =1000

a) The point estimate of the population proportion is _. ​(Round to the nearest thousandth as​ needed.)

b) The margin of error is _. ​(Round to the nearest thousandth as​ needed.)

c) The number of individuals in the sample with the specified characteristic is _. ​(Round to the nearest integer as​ needed.)

Answer 1

Solutions:
Given that .
n=1000
Lower bound: 0.593
Upper bound: 0.867

a)
Point estimate= p^= (Upper bound+ lower bound)/2
=(0.867+0.593)/2
= 0.73
=0.7300 (Round to the nearest thousandth as​ needed.)

Answer a) The point estimate of the population proportion is 0.7300 ​(Round to the nearest thousandth as​ needed.)
b)
Margin of error= upper bound- p^
= 0.867 - 0.7300
=0.137
= 0.1370 (Round to the nearest thousandth as​ needed.)
Answer b) The margin of error is 0.1370 ​(Round to the nearest thousandth as​ needed.)
c)
X= np^
= 1000×0.7300
= 730
The number of individuals in the sample with the specified characteristic is. 730 (Round to the nearest integer as​ needed)