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 0.06 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 9 out of 90 people have blood type B.
  medical filesFor 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 0.06 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 9 out of 90 people have blood type B.
  medical files

Answer 1

Solution,

Given that,

= 1 - = 0.5

margin of error = E = 0.06

At 85% confidence level

= 1 - 85%

= 1 - 0.85 =0.15

/2 = 0.075

Z/2 = Z0.075  = 1.44

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

= (1.44 / 0.06)2 * 0.5 * 0.5

sample size = n = 144

b) = 0.10

1 - = 1 - 0.10 = 0.90

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

= (1.44 / 0.06)2 * 0.10 * 0.90

n = 51.84

sample size = n = 52