Question

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 90% sure that the point estimate p̂ will be within a distance of 0.058 from p?

b.) Answer part (a) if you use the preliminary estimate that about 14 out of 90 people have blood type B.

Answer 1

a)
The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.058

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.1 is 1.64.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.64/0.058)^2
n = 199.88

sample size = 200

b)
p = 14/90 = 0.1556

n >= p*(1-p)*(zc/E)^2
n = 0.1556*(1 - 0.1556)*(1.64/0.058)^2
n = 105.05

sample size = 105