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Analyzing Voter Demographics: Independence & Exclusivity
Chapter 4, Problem 36(choose chapter or problem)
The following data represent political party by age from a random sample of registered Iowa Voters.
\(\begin{array}{|lcccrc} & \mathbf{1 7 - 2 9} & \mathbf{3 0 - 4 4} & \mathbf{4 5 - 6 4} & \mathbf{6 5 +} & \text { Total } \\ \hline \text { Republican } & 224 & 340 & 1075 & 561 & \mathbf{2 2 0 0} \\ \hline \text { Democrat } & 184 & 384 & 773 & 459 & \mathbf{1 8 0 0} \\ \hline \text { Total } & \mathbf{4 0 8} & \mathbf{7 2 4} & \mathbf{1 8 4 8} & \mathbf{1 0 2 0} & \mathbf{4 0 0 0} \end{array}\)
(a) Are the events “Republican” and “30–44” independent? Justify your answer.
(b) Are the events “Democrat” and “65+” independent? Justify your answer.
(c) Are the events “17–29” and “45–64” mutually exclusive? Justify your answer.
(d) Are the events “Republican” and “45–64” mutually exclusive? Justify your answer.
Questions & Answers
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QUESTION:
The following data represent political party by age from a random sample of registered Iowa Voters.
\(\begin{array}{|lcccrc} & \mathbf{1 7 - 2 9} & \mathbf{3 0 - 4 4} & \mathbf{4 5 - 6 4} & \mathbf{6 5 +} & \text { Total } \\ \hline \text { Republican } & 224 & 340 & 1075 & 561 & \mathbf{2 2 0 0} \\ \hline \text { Democrat } & 184 & 384 & 773 & 459 & \mathbf{1 8 0 0} \\ \hline \text { Total } & \mathbf{4 0 8} & \mathbf{7 2 4} & \mathbf{1 8 4 8} & \mathbf{1 0 2 0} & \mathbf{4 0 0 0} \end{array}\)
(a) Are the events “Republican” and “30–44” independent? Justify your answer.
(b) Are the events “Democrat” and “65+” independent? Justify your answer.
(c) Are the events “17–29” and “45–64” mutually exclusive? Justify your answer.
(d) Are the events “Republican” and “45–64” mutually exclusive? Justify your answer.
ANSWER:Step 1 of 5
The following data represent political party by age from a random sample of registered Iowa Voters.
|
|
17-29 |
30-44 |
45-64 |
65+ |
Total |
|
Republican |
224 |
340 |
1075 |
561 |
2200 |
|
Democrat |
184 |
384 |
773 |
459 |
1800 |
|
Total |
408 |
724 |
1848 |
1020 |
4000 |
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Analyzing Voter Demographics: Independence & Exclusivity
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Analyze the relationships between different political affiliations and age groups. Determine whether certain events are independent, mutually exclusive, or neither, based on the provided probabilities. The findings offer a nuanced understanding of voter demographics and their interdependencies.
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