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 p̂ will be within a distance of 0.04 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 13 out of 90 people have blood type B.
_________ medical files

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.04

At 85% confidence level

= 1 - 85%

= 1 - 0.85 =0.15

/2 = 0.075

Z_/2 = Z_0.075 = 1.44

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.44 / 0.04)² * 0.5 * 0.5

sample size = n = 324

b) = 13 / 90 = 0.144

1 - = 1 - 0.144 = 0.856

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.44 / 0.04)² * 0.144 * 0.856

= 159.75

sample size = n = 160