Answer to Question #263683 in Statistics and Probability for mick

Question

Determine the sample size necessary to estimate a population proportion to within 0.03 with 90%

confidence assuming you have no knowledge of the approximate value of the population proportion.

(b)    Using the sample size obtained in (a) and pˆ = 0.75

Estimate the population with 90% confidence

Answer 1

(a):

Margin of error (E) = 0.03

Z value at 90% confidence interval = 1.645

$E=Z\times\sqrt{\frac{p\times(1-p)}{n}}$

$0.03=1.645\times\sqrt{\frac{0.5\times(1-0.5)}{n}}$

Square both sides;

$0.0009=2.71\times\frac{0.5\times(1-0.5)}{n}$

$n= \frac{2.71\times0.25}{0.0009}=751.67$

Sample size = 752

(b):

pˆ = 0.75

sample size = 752

$p\pm Z\times\sqrt{\frac{p\times(1-p)}{n}}$

$0.75\pm 1.645\times\sqrt{\frac{0.75\times(1-0.75)}{752}}$

$0.75\pm0.026$

0.724 to 0.776