Question

1. If, based on a sample size of 850, a political candidate finds that 458 people would vote for him in a two-person race, what is the 95% confidence interval for his expected proportion of the vote

Answer 1

Answer:

The 95% confidence interval is

    $0.5055<  p <0.5725$

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  850

  The number of can of people that will vote in a two people race is k =  458

Generally the sample proportion is mathematically represented as

        $\^ p = \frac{k}{n}$

=>     $\^ p = \frac{458}{850}$

=>     $\^ p = 0.539$

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   is  

   $Z_{\frac{\alpha }{2} } =  1.96$

Generally the margin of error is mathematically represented as  

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

=>   $E = 1.96 *  \sqrt{\frac{0.539(1- 0.539)}{850} }$

=>  $E =  0.0335$

Generally 95% confidence interval is mathematically represented as  

             $\r p -E <  p <  \r p +E$

=>          $0.539 - 0.0335<  p < 0.539 + 0.0335$

=>          $0.5055<  p <0.5725$