Question

In a randomly selected sample of 500 registered voters in a community, 260 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.)
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(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.)
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Answer 1

The statistic software output for this problem is:

One sample proportion summary confidence interval: P: Proportion of successes Method: Standard-Wald 95% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit 260 500 0.52 0.022342784 0.47620895 0.56379105

One sample proportion summary confidence interval: p: Proportion of successes Method: Standard-Wald 98% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit 260 500 0.52 0.022342784 0.46802291 0.57197709

(a) sample proportion = 0.52

(b) standard error = 0.022

(c) The 95% CI is : (0.476 , 0.564)

(d)The 98% CI is :(0.468 , 0.572)