Answer:
The 95% confidence interval of the proportion of Americans who believe in the conspiracy is [tex] 0.551< p < 0.610[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n =1057
The number that believe there was a conspiracy is k = 614
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{614}{1057 }[/tex]
=> [tex]\^ p = 0.5809[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.96 * \sqrt{\frac{0.5809 (1- 0.5809)}{1057} } [/tex]
=> [tex]E = 0.02975 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.5809 - 0.02975< p < 0.5809 + 0.02975[/tex]
=> [tex] 0.551< p < 0.610[/tex]
