Question

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 2% of the true population proportion. how large of a sample size is required

Answer 1

Answer:

The value is  $n =2401$

Step-by-step explanation:

From the question we are told that  

 The  margin of error is  E = 2%= 0.02

From the question we are told the confidence level is  95% , hence the level of significance is    

      $\alpha = (100 - 95 ) \%$

=>   $\alpha = 0.05$

Generally from the normal distribution table the critical value  of  $\frac{\alpha }{2}$ is  

   $Z_{\frac{\alpha }{2} } = 1.96$

Here we are going to assume that the sample proportion is  $\^ p = 0.50$

  Generally the sample size is mathematically represented as  

    $n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=>   $n =[\frac{ 1.96 }{ 0.02} ]^2 * 0.5 (1 -0.5 )$

=>    $n =2401$