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Exit Poll Analysis: Education Funding Referendum Votes
Chapter 5, Problem 21(choose chapter or problem)
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 310 voters finds that 164 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49? Based on your result, on the dangers of using exit polling to call elections. Include a discussion of the potential nonsampling error that could disrupt your findings.
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QUESTION:
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 310 voters finds that 164 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49? Based on your result, on the dangers of using exit polling to call elections. Include a discussion of the potential nonsampling error that could disrupt your findings.
ANSWER:Step 1 of 2
Given, n=310 , p = 0.49
A random sample of 310 voters which is less than 5% of the population.
\(\begin{aligned}
\mathrm{np}(1-\mathrm{p}) & =310(0.49)(1-0.49) \\
& =77.469 \simeq 77.47
\end{aligned}\)
The distribution of \(\widehat{p}\) is approximately normal, with mean \(\mu_{p}=0.49\) and the standard deviation
\(\sigma_{\widehat{p}}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.49(1-0.49)}{310}}=0.0284\)
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Exit Poll Analysis: Education Funding Referendum Votes
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Explore the application of proportion z-tests in analyzing exit polling data. Understand how to determine the likelihood of sample results given a population proportion. Recognize the importance of considering non-sampling errors in interpreting exit poll outcomes.