Question

In a randomly selected sample of 500 registered voters in a community, 120 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

Solution:

Given: Totally there are 500 registered voters in which 120 individuals say that they plan to vote for Candidate Y in the upcoming election.

a)The sample proportion planning to vote for Candidate Y is =120/500=0.24

b)Formula to find standard error of sample proportion is:

SE=(1-)/n where =observed value of sample proportion and n=sample size=500

SE=(1-)/n=[0.24(1-0.24)]/500=0.019

c)For 95% confidence interval, z=1.96

Confidence interval is [-z*SE] and [+z*SE]

[0.24-(1.96*0.019)] and [0.24+(1.96*0.019)]

So 95% confidence interval is [0.203,0.277]

d)For 98% confidence interval, z=2.33

Confidence interval is [-z*SE] and [+z*SE]

[0.24-(2.33*0.019)] and [0.24+(2.33*0.019)]

So 98% confidence interval is [0.196,0.284]