Question

video A population proportion is.40. A sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion. Use z-table. Round your answers to four decimal places a. what is the probability that the sample proportion will be within ±.03 of the population proportion? (Round z value in intermediate calculations to 2 decimal places.) b. what is the probability that the sample proportion will be within ±.05 of the population proportion? (Round z value in intermediate calculations to 2 decimal places.)

Answer 1

The margin of error of a single proportion = $Z_{\alpha /2}\sqrt{\frac{p(1-p)}{n}}$

a) 0.03 = $Z_{\alpha /2}\sqrt{\frac{0.4(1-0.4)}{200}}$

$Z_{\alpha /2}$ = 0.866

probability = P(-0.866 < $Z_{\alpha /2}$ <0.866) = P(0.866) - P(-0.866) = 0.6135

b) 0.05 = $Z_{\alpha /2}\sqrt{\frac{0.4(1-0.4)}{200}}$

$Z_{\alpha /2}$ = 1.44

probability = P(-1.44 < $Z_{\alpha /2}$ <1.44) = P(1.44) - P(-1.44) = 0.8501