The mayor of a town has proposed a plan for the construction of a new bridge.  A political study took a sample of 900900 voters in the town and found that 60%60% of the residents favored construction.  Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 56%56%.  State the null and alternative hypotheses.

In this scenario, you are dealing with a hypothesis test for proportions. The goal is to test whether the percentage of residents who favor construction is more than 56%.

### Null and Alternative Hypotheses:
- **Null Hypothesis (\(H_0\))**: The percentage of residents who favor construction is **equal to** 56%.
  \[
  H_0: p = 0.56
  \]
- **Alternative Hypothesis (\(H_a\))**: The percentage of residents who favor construction is **greater than** 56%.
  \[
  H_a: p > 0.56
  \]

Here, \(p\) represents the true proportion of residents in the town who favor the construction of the bridge.

The test will be a **one-tailed test** (right-tailed) because the alternative hypothesis is testing whether the proportion is greater than 56%.

Would you like help on the next steps for testing this hypothesis?

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Here are five questions that expand on this concept:
1. What is the test statistic used for hypothesis testing of proportions?
2. How do you calculate the p-value in a one-tailed test for proportions?
3. What is the importance of the significance level (\(\alpha\)) in hypothesis testing?
4. How would you calculate the confidence interval for the proportion of voters favoring the bridge?
5. How would the result change if the sample size were smaller?

**Tip**: Always check if the sample size is large enough to assume normality when performing hypothesis tests on proportions (use \(np \geq 5\) and \(n(1-p) \geq 5\) criteria).

The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 900 voters in the town and found that 60% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 56%. State the null and alternative hypotheses.

Learn how to test the hypothesis that more than 56% of the town residents favor the construction of a new bridge. Using a sample of 900 voters and key statistical concepts like hypothesis testing and proportions, this problem provides a detailed solution for Grades 11-12 students.

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