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AP® Statistics

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Upcoming Election

APSTAT-HYFPPA

The mayor of a large city is considering running for reelection.

She won the previous election against her competitor $52\%$ to $48\%$.

Last week, two independent, random samples were taken of likely voters, each of size n = $50$. These polls found the proportion of likely voters to vote for the current mayor is $48\%$ and $50\%$, respectively.

Assume she is running against one other candidate and needs the majority of votes to win.

Individually, which of the following statements is true about these samples?

A

Both samples give sufficient evidence that she will NOT be reelected.

B

The mayor still could easily get $52\%$ of the vote on election day, as getting samples of size n = $50$ at $50\%$ and $48\%$ could easily happen by chance.

C

The sample containing $48\%$ is convincing evidence she will NOT be reelected, but the $50\%$ sample fails to give such evidence.

D

Since a sample found her getting less than the majority vote, the mayor will be very likely to lose.

E

These samples give strong evidence the mayor will NOT lose the upcoming race and still has $52\%$ of the vote, as these values could have easily happened by chance.