A random sample of likely voters showed that 60% planned to vote for Candidate X

Question

A random sample of likely voters showed that 60% planned to vote for Candidate X, with a margin of error of 4 percentage points and with 95% confidence. Use a carefully worded sentence to report the 95% confidence interval for the percentage of voters who plan to vote for Candidate X. Is there evidence that Candidate X could lose? Suppose the survey was taken on the streets of a particular city and the candidate was running for president of the country that city is in. Explain how that would affect your conclusion.

Explanation / Answer

A)

We are 95% confident that 56% to 64% of voters would vote for candidate X in the next election.

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b)

At 95% confidence, there is no significant evidence that candidate X would lose, at the whole interval is greater than 50%.

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c)

Since the candidate is popular in that city, then the sample obtained may not be a good representative of the whole nation. Hence, we may overestimate the proportion of people who will vote for candidate X.

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