Question

# A random sample of medical files is used to estimate the proportion p of all people...

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 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.

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