Answer:
The 99% confidence interval is  [tex] 0.4023  <  p < 0.5157[/tex]
Step-by-step explanation:
From the question we are told that
    The sample size is  n = 514
    The sample proportion is  [tex]\^ p = 0.459[/tex]
   Â
From the question we are told the confidence level is  99% , hence the level of significance is  Â
   [tex]\alpha = (100 - 99 ) \%[/tex]
=> Â [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is Â
  [tex]Z_{\frac{\alpha }{2} } =  2.58[/tex]
Generally the margin of error is mathematically represented as Â
   [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> Â [tex]E =2.58 * \sqrt{\frac{0.459 (1- 0.459)}{514} } [/tex]
=> Â Â [tex]E =0.0567 Â [/tex]
Generally 99% confidence interval is mathematically represented as Â
   [tex] 0.459  -0.0567 <  p < 0.459  + 0.0567[/tex]
=> Â Â [tex] 0.4023 Â < Â p < 0.5157[/tex]
