Determine the point estimate of the population proportion, the margin of error f

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

boundequals=0.503,

upper

boundequals=0.797,

nequals=1200

The point estimate of the population proportion is

nothing.

(Round to the nearest thousandth as needed.)

The margin of error is

nothing.

(Round to the nearest thousandth as needed.)

The number of individuals in the sample with the specified characteristic is

nothing.

(Round to the nearest integer as needed.)

Explanation / Answer

given:

sample prop-margin of error=0.503

sample prop+margin of error=0.797

add 2 eq

2(sample prop)=0.503+0.797

2(sample prop)=1.3

sample prop=1.3/2=0.65

sample proprtion=0.65

Solutionb:

sub sample prop in eq1

sample prop-margin of error=0.503

0.65-0.503=margin of error

0.147=margin of error

margin of error=0.147

Solutionc:

nmargin of error=0.147

zcrit(sqrt(p^(1-p^)/n)=0.147

1.96 sqrt(0.65(1-0.65)/n=0.147

sqrt(0.65*0.35/n)=0.075

squaring on both sides

0.2275/n=0.075^2

n=0.2275/0.075

n=40.44

n=40

The number of individuals in the sample with the specified characteristic=40

n=40.44

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