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Chapter 7: Problem 67

In the 1960 presidential election, \(34,226,731\) people voted for Kennedy, \(34,108,157\) for Nixon, and 197,029 for third-party candidates (Source: www.uselectionatlas.org). a. What percentage of voters chose Kennedy? b. Would it be appropriate to find a confidence interval for the proportion of voters choosing Kennedy? Why or why not?

Short Answer

Expert verified
a. To find out Kennedy's voting percentage, the equation is as follows: \[ Percentage = \frac{{34,226,731}}{{68,531,917}} \times 100 \]. Feel free to proceed with this calculation. b. No, it would not be appropriate. Confidence intervals are used when dealing with uncertain or incomplete data, such as samples from larger populations. However, in this case, we have exact numbers for the entire population of voters in this particular election, so there's no uncertainty or need for estimation.

Step by step solution

01

Calculate Kennedy's Voting Percentage

To calculate the percentage of voters that chose Kennedy, divide the number of votes for Kennedy by the total number of votes and then multiply by 100: \[Percentage = \frac{{Number of votes for Kennedy}}{{Total votes}} \times 100 = \frac{{34,226,731}}{{34,226,731 + 34,108,157 + 197,029}} \times 100\]
02

Simplify the Equation

Simplify the equation to get the percentage of voters who chose Kennedy: \[Percentage = \frac{{34,226,731}}{{68,531,917}} \times 100\]
03

Solve for Kennedy's Voting Percentage

After performing the calculation you acquire the percentage for Kennedy's votes.
04

Deciding if a Confidence Interval Would be Appropriate

Since every single vote in this election has been taken into account, this data represents a population, not a sample. You're given exact, not estimated, numbers. Hence, it's unnecessary to calculate the confidence interval because it's used when dealing with uncertain or incomplete data, such as samples from larger populations.

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