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 0.03 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 9 out of 90 people have blood type B.
medical files

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 0.03

At 85% confidence level

= 1 - 85%

=1 - 0.85 =0.15

/2 = 0.075

Z/2 = 1.44

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

= (1.44 / 0.03)² * 0.5 * 0.5

   sample size = n = 576 medical files

b) n = 90

x = 9

Point estimate = sample proportion = = x / n = 9 / 90 = 0.10

1 - = 1 - 0.10 = 0.90

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

= (1.44 / 0.03)² * 0.10 * 0.90

n = 207.36

sample size = n = 208 medical files