Answer:
The 90% confidence interval is  [tex] 0.8315 <  p < 0.8685[/tex]
Step-by-step explanation:
From the question we are told that
  The sample size is n =  1007 Â
  The sample proportion is  [tex]\^ p = 0.85[/tex]
From the question we are told the confidence level is  90% , hence the level of significance is  Â
   [tex]\alpha = (100 - 90 ) \%[/tex]
=> Â [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is Â
  [tex]Z_{\frac{\alpha }{2} } =  1.645[/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 =1.645 * \sqrt{\frac{0.85 (1- 0.85 )}{1007}} [/tex]
=> Â [tex]E = 0.0185 [/tex] Â Â
Generally 90% confidence interval is mathematically represented as Â
   [tex]\^ p -E <  p <  \^ p +E[/tex]
=> Â [tex]0.85 -0.0185 < Â p < 0.85 + 0.0185[/tex]
=> Â [tex] 0.8315 < Â p < 0.8685[/tex]
