Answer:
The confidence interval is [tex]0.2857< p < 0.4601[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 118
The number that gave the correct answer is k = 44
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{44}{118}[/tex]
=> [tex]\^ p =0.3729[/tex]
Generally given that the confidence level is 95% the level of significance is mathematically represented as
[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{0.3729(1 - 0.3729)}{118} }[/tex]
=> [tex]E = 0.0872 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.3729 -0.0872< p < 0.3729 +0.0872[/tex]
=> [tex]0.2857< p < 0.4601[/tex]
