3. It seems to you that fewer than half of people who are registered voters in t

Question

3. It seems to you that fewer than half of people who are registered voters in the City of Madison do in fact vote when there is an election that is not for the president. You would like to know if this is true. You take an SRS of 200 registered voters in the City of Madison, and discover that 122 of them voted in the last non-presidential election (a) How might a simple random sample have been gathered? (b) Construct a 95% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections (c) Interpret the interval you created in part (b (d) Based on your CI, does it seem that fewer than half of registered voters in the City of Madison vote in non-presidential elections? Explain

Explanation / Answer

p = 122/200 = 0.61

B) At 95% confidence interval the critical value is z0.025 = 1.96

The 95% confidence interval for true proportion is

p +/- z0.025 * sqrt( p * (1 - p )/n )

= 0.61 +/- 1.96 * sqrt(0.61 * 0.39/200)

= 0.61 +/- 0.068

= 0.542, 0.678

C) We are 95% confidence that the true population lies between the interval.

D) 100/200 = 0.5

As the confidence interval doesn't contain the proportion value 0.5, so it doesn't seem that fewer than half of registered voters in the city of Madison vote in non-presidental election.

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