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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 95% confident that you estimate is within 3.5% of the true population proportion. How large of a sample size is required?

Respuesta :

baraltoa

Answer:

n Ā = 400

Step-by-step explanation:

The formula for the error in our estimate is given by:

Standard Error : Ā āˆš ( p(1-p)/ n)

Error = Ā SE = ZĪ±/2 Ā  āˆš ( p(1-p)/ n) Ā where

ZĪ±/2= critical Ā value for 95% confidence level = 1.96

and we know our error is 3.5 %

But we do not the sample proportion p. Then what we can do is give an estimate of p in the absence of any other information.

In this case we will use p= 0.5 which is the value that maximizes the expression for the standard error :

if p = 0.8 then SE= 0.040

Ā  p = 0.3 then SE =0.036

Ā  p = 0.1 then Ā SE = 0.030

Ā  p = 0.5 then SE = 0.050

Substituting

3.5/100 Ā = 1.96 x Ā āˆš (( 0.5 x 0.5 ) /n )

3.5/ (100 x 1.96 x 0.5 ) = 1/ āˆšn

0.0357 = 1 /āˆšn

n = 20Ā²

n = 400

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