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=0.691, upper bound=0.891, n=1000. The number of individuals in the sample with the specified characteristic is? Round to the nearest integer as needed

Answer 1

Solution

Given a confidence interval for the proportion is

Lower bound = 0.691

Upper bound = 0.891

i.e. interval is (0.691,0.891)

The confidence interval is nothing but

point estimate Margin of error

i.e. Lower bound = point estimate - Margin of error

and upper bound = point estimate + Margin of error

Solving these two equations,we get

point estimate =

=

= 0.791

And ,

Margin of error =

=   

= 0.100

Now, n = 1000 given.

The number of individuals in the sample with the specified characteristic is n*point estimate of the population proportion

i.e. x = 1000 × 0.791

x = 791