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

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
Statistics

Formulas

Null hypothesis: H0: p ≤ p0
Alternative hypothesis: H1: p > p0
Test statistic for proportion: z = (p̂ - p0) / sqrt[(p0 * (1 - p0)) / n]

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12, College Level