Question

Ben “Ice Town” Wyatt is running for the office of Mayor against heavy opposition from his lone opponent in a close race. It is believed that he may lose the election and is expected to pick up only 48% of the vote. Days before the election, 100 voters are polled in a preliminary sample. In the sample, 52 of the 100 voters say they plan to vote for Wyatt over his opponent in the upcoming election.

a). What are the values of p̂ and n? p̂ = ________ , n = ________

b). Construct a 95% confidence interval for the population proportion from the sample data. Round your answer to three decimal places. ( _________________ , _________________ ).

c). Based on your confidence interval above, are you confident that “Ice Town” will win the election? (Yes or No) __________.

d). Assuming the candidate can indeed pick up 52% of the vote, how large of a sample of voters would be needed to be 95% confident that “Ice Town” Wyatt would indeed win the election with less than a 2% margin of error? ?≥ ____________.

Answer 1

a). the values of p̂ and n are :-

b).z critical value for 95% confidence level, both tailed test be:-

the 95% confidence interval for the population proportion from the sample data is :-

c).YES,Based on the confidence interval above, i am confident that “Ice Town” will win the election.

d).given data are:-

p = 0.52

margin of error (E) = 0.02

the needed sample size is:-

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