Math Problem Statement
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.
Solution
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 (): The percentage of residents who favor construction is equal to 56%.
- Alternative Hypothesis (): The percentage of residents who favor construction is greater than 56%.
Here, 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?
Here are five questions that expand on this concept:
- What is the test statistic used for hypothesis testing of proportions?
- How do you calculate the p-value in a one-tailed test for proportions?
- What is the importance of the significance level () in hypothesis testing?
- How would you calculate the confidence interval for the proportion of voters favoring the bridge?
- 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 and criteria).
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Proportions
One-tailed Test
Formulas
Null Hypothesis: H₀: p = 0.56
Alternative Hypothesis: Hₐ: p > 0.56
Theorems
Central Limit Theorem
Law of Large Numbers
Suitable Grade Level
Grades 11-12
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