Conduct a poll for candidate. You ask 55 if they support the candidate and 295 s

Question

Conduct a poll for candidate. You ask 55 if they support the candidate and 295 say they support the claim. What is 95% confidence level for the true rate the candidate has support?
0.641-0.715 0.402-0.485 0.307- 0.391 0.661- 0.744 0.494- o.578 0.326- 0.411 Conduct a poll for candidate. You ask 55 if they support the candidate and 295 say they support the claim. What is 95% confidence level for the true rate the candidate has support?
0.641-0.715 0.402-0.485 0.307- 0.391 0.661- 0.744 0.494- o.578 0.326- 0.411
0.641-0.715 0.402-0.485 0.307- 0.391 0.661- 0.744 0.494- o.578 0.326- 0.411

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.536363636          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.021263613          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.49468772          
upper bound = p^ + z(alpha/2) * sp =    0.578039552          
              
Thus, the confidence interval is              
              
(   0.494 ,   0.578 ) [option e]

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