Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that your estimate is within 0.1% of the true population proportion. How large of a sample size is required?

Answer #1

Solution :

Given that,

= 0.5 ( when estimate is not given then use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.01% = 0.0001

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_{/2}
= Z_{0.05} = 1.645

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.645 */0.0001)^{2} * 0.5 *0.5

=67650625

Sample size = 67650625

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