A researcher wishes to estimate the proportion of adults who

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 95% confidence if

a)?she uses a previous estimate of 0.56?

b)?she does not use any prior estimates?

A)n=___

(Round up to the nearest integer.)

b) n=___

(Round up to the nearest integer.)

Solution

(a) Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.01)^2*0.56*(1-0.56)

=9465.702

Take n=9466

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(b) We use p=0.5 as estimated.

So n=(Z/E)^2*p*(1-p)

=(1.96/0.01)^2*0.5*(1-0.5)

=9604

Take n=9604