Question

Estimating Sample Size: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 54 % . You would like to be 90% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required? (please do not do any intermediate rounding)

Answer 1

Answer:

The value is $n = 2887$

Step-by-step explanation:

From the question we are told that

  The population proportion is  $p = 0.54$

   The margin of error is  $E = 1.5 \% = 0.015$

From the question we are told the confidence level is  90% , hence the level of significance is    

      $\alpha = (100 - 90 ) \%$

=>   $\alpha = 0.10$

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

   $Z_{\frac{\alpha }{2} } =  1.645$

Generally the sample size is mathematically represented as

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

=>        $n = [\frac{1.645 }{0.015} ]^2 * 0.54(1-0.54)$

=>        $n = 2887$