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

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