Question

In a randomly selected sample of 500 registered voters in a community, 320 individuals say that they plan to vote for Candidate Y in the upcoming election.

(a) Find the sample proportion planning to vote for Candidate Y. (Round your answer to two decimal places.)


(b) Calculate the standard error of the sample proportion. (Round your answer to three decimal places.)


(c) Find a 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.)

(d) Find a 98% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.)

Answer 1

a) The sample proportion planning to vote for Candidate Y is

b) the standard error of the sample proportion is

$SE_{\widehat{p}} = \sqrt{\frac{\widehat{p}\widehat{q}}{n}} =\sqrt{0.64*0.36/500} =0.021$

c) 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y is

$\widehat{p} \pm Z\times SE_{\widehat{p}} =0.64\pm 1.96\times 0.021$

$=0.64\pm0.042$

= (0.598, 0.682)

d) 98%  confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y

$\widehat{p} \pm Z\times SE_{\widehat{p}} =0.64\pm 2.327\times 0.021$

$=0.64\pm0.049$

= (0.591, 0.689)