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In this scenario, we are setting up hypotheses to test whether the seat-belt compliance rate in a particular state has increased since it was recorded as 76% in 2008.

To define the hypotheses:

1. **Parameter:** Let \( p \) represent the current seat-belt compliance rate in this state.

2. **Null Hypothesis (\( H_0 \)):** The compliance rate has not increased, meaning it is still at or below 76%.
   \[
   H_0: p = 0.76
   \]

3. **Alternative Hypothesis (\( H_A \)):** The compliance rate has increased, meaning it is greater than 76%.
   \[
   H_A: p > 0.76
   \]

So, the hypotheses would be:
- **\( H_0: p = 0.76 \)**
- **\( H_A: p > 0.76 \)**

Would you like a more detailed explanation of hypothesis testing, or have any other questions on this?

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Here are 5 related questions to consider:
1. How is a p-value used to determine if we reject the null hypothesis?
2. What statistical test would be appropriate to test this hypothesis?
3. What sample size is required to detect a significant difference if the true compliance rate is, say, 80%?
4. How does changing the level of significance affect the results of hypothesis testing?
5. What are the possible outcomes if we decide to fail to reject the null hypothesis?

**Tip:** In hypothesis testing, always clearly define the parameter (like \( p \) in this case) to avoid confusion in interpreting results.

For each of the given situations, define the parameter and write the null and alternative hypotheses in terms of parameter values. Complete parts a through d.

(a) Seat-belt compliance in a certain state was 76% in 2008. The state wants to know if it has increased.

Learn how to set up null and alternative hypotheses to test if the seat-belt compliance rate has increased since 2008, where the initial rate was 76%. This example covers key statistical concepts such as hypothesis testing and proportions, suitable for undergraduate students.

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