Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of medical files is used to estimate the proportion p of all people who have blood type B. (a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.) medical files (b) Answer part (a) if you use the preliminary estimate that about 8 out of 90 people have blood type B. medical files Need Help? Read It

Answer 1

a) The margin of error given is

ΜΕ = 0,06

$ME=Z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n}}$

for 85% confidence $Z_{\frac{\alpha }{2}}=1.4395$ ( using excel formula =NORM.S.INV(0.925))

since prior estimate is not given we assume p = 0.5

$n= (\frac{1.4395}{0.06})^2*0.5*0.5\approx 144$

b) $p=\frac{8}{90}=0.0889$ is known now so

$n= (\frac{1.4395}{0.06})^2*0.0889(1-0.0889)\approx 47$