Math Problem Statement
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 15001500 voters in the town and found that 74%74% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 71%71%. State the null and alternative hypotheses.
Solution
To test the claim about the percentage of residents who favor annexation, we need to set up the null hypothesis () and the alternative hypothesis ().
Hypotheses:
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Null Hypothesis (): The percentage of residents who favor annexation is equal to 71%.
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Alternative Hypothesis (): The percentage of residents who favor annexation is greater than 71%.
Explanation:
- The null hypothesis represents the status quo or no effect—in this case, that the proportion of residents favoring annexation is 71%.
- The alternative hypothesis represents the claim or research question we are testing—that the proportion is greater than 71%.
- This is a one-tailed test because the strategist is specifically testing for an increase (greater than 71%).
Do you want to proceed with calculating the test statistic and p-value? Let me know!
Here are 5 related questions to expand your understanding:
- What is the significance level () for this test?
- How is the test statistic calculated for a proportion hypothesis test?
- What is the critical value for a one-tailed test at a common significance level (e.g., 0.05)?
- How does sample size affect the hypothesis test in this scenario?
- What would the conclusion be if the p-value is less than ?
Tip: Always ensure your alternative hypothesis aligns with the
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Proportions
Statistics
Formulas
Null Hypothesis: H0: p = p0
Alternative Hypothesis (One-tailed test): Ha: p > p0
Z-test for proportion: z = (p̂ - p0) / √(p0(1 - p0) / n)
Theorems
Central Limit Theorem
Standard Normal Distribution
Suitable Grade Level
Grades 10-12, College Level
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