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 equals=0.3880.388​,

upper bound equals=0.5920.592​,

n equals=1200

Answer 1

Solution:

We know , the confidence interval is nothing but

Point estimate Margin of error

So ,

Lower bound = Point estimate - Margin of error

Upper bound = Point estimate + Margin of error

1) Point estimate = (Upper bound + Lower Bound)/2

= (0.592 + 0.388)/2

= 0.49

2) Margin of error = (Upper bound - Lower Bound)/2

= (0.592 - 0.388)/2

=0.102

3) Given that

n = 1200

We know that = x/n

So , x = n * = n * Point estimate = 1200 *  0.49 = 588

the number of individuals in the sample with the specified​characteristic x = 588