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 boundequals0.423, upper boundequals0.677, nequals1500 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

lower bound =0.423

upper bound =0.677

a) point estimate =(lower bound +upper bound)/2

                              =(0.423+0.677)/2

                              =1.1/2

                              =0.55

b) Margin of error =(upper bound -lower bound)/2

                              =(0.677-0.423)/2

                              =0.254/2

                              =0.127

c) Assuming a 95% confidence interval

E=Z/2 × [(p×q)/n]

0.127 =1.96 x (0.55×0.45)/n

0.127 =0.975087 /n

n =0.975087/0.127

n =7.67785

n=(7.67785)^2

n=59

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