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=0.436

upper bound=0.694

n=1000

Answer 1

Given that, Lower bound = 0.436

Upper bound = 0.694 and sample size ( n ) = 1000

Point estimate of the population proportion is,

= (Upper bound + Lower bound) / 2

= (0.694 + 0.436) / 2

= 1.13 / 2

= 0.565

=> Point estimate = 0.565

Margin of error ( E ) is,

E = (Upper bound - Lower bound) / 2

= (0.694 - 0.436) / 2

= 0.258 / 2

= 0.129

=> Margin of error  = 0.129

The number of individuals in the sample with the specified​ characteristic, X is,

X = point eatimate * sample size = 0.565 * 1000 = 565

=> X = 565