Answer:
The sample size bedded is  [tex]n =41[/tex]
Step-by-step explanation:
From the question we are told that
  The margin of error is  [tex]E = 0.100[/tex]
  The sample proportion is  [tex]\^ p = 0.45[/tex]
From the question we are told the confidence level is  80% , hence the level of significance is  Â
   [tex]\alpha = (100 - 80) \%[/tex]
=> Â [tex]\alpha = 0.20[/tex]
Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is Â
  [tex]Z_{\frac{\alpha }{2} } =  1.282[/tex]
Generally the sample size is mathematically represented as Â
  [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.282}{ 0.100} ]^2 *0.45 (1 - 0.45 ) [/tex]
=> [tex]n =41[/tex]
