In a randomly selected sample of 500 registered voters in a community, 300 indiv

Question

In a randomly selected sample of 500 registered voters in a community, 300 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.) 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. to

Explanation / Answer

a) sample proportion is p=300/500=0.6

b) standard error is given SE= sqrt(p*(1-p)/N)=sqrt(0.6*0.4/500)=0.0219

c) for 95% confidence, the z value is 1.96, thus lower limit is p-z*SE =0.6-1.96*0.0219=0.5571

upper limit is p+z*SE=0.6+1.96*0.0219=0.6429

d) for 98% confidence, the z value is 2.33, thus the lower limit is p-z*SE =0.6-2.33*0.0219=0.54897

upper limit is  p+z*SE =0.6+2.33*0.0219=0.651027

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