Suppose you want to estimate the proportion of traditional c

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what the proportion might be.

a) What sample size is needed if you wish to be 95% confident that your estimate is within .02 of the true proportion?

b) What sample size is needed if you wish to be 99% confident that you

Solution

a) What sample size is needed if you wish to be 95% confident that your estimate is within .02 of the true proportion?

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

We use p=0.5 as estimated.

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

=(1.96/0.02)^2*0.5*0.5

=2401

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b) What sample size is needed if you wish to be 99% confident that you