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=0.507​,

upper bound=0.903​,

n=1000

The margin of error is _____.

Answer 1

Let p be the point estimate of the population proportion and m be the margin of error.

Now we know that, the confidence interval for the population proportion is given by (LB,UB) where LB is the lower bound of the confidence interval= p-m and UB is the upper bound of the coficonfid interval = p+m.

Thus,

UB-LB = 2m

Or, m = (UB-LB)/2.

Here LB is .507 and UB is given to be .903.

Hence margin of error is (.903 - .507)/2 = .198

Hence the required margin of error is 0.198.

Hope the solution helps. Thank you.