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For this problem, the task is to define the parameter and write the null and alternative hypotheses for the given scenario, which involves a slot machine win rate.

### Solution:
The problem states:
> A casino wants to know if their slot machine really delivers the 3 in 100 win rate that it claims.

1. **Define the Parameter**:
   Let \( p \) represent the proportion of wins in the casino's slot machine.

2. **Null Hypothesis ( \( H_0 \) )**:
   Since the casino claims a win rate of 3 in 100, which is equivalent to 0.03, the null hypothesis assumes that the win rate is indeed 0.03:
   \[
   H_0: p = 0.03
   \]

3. **Alternative Hypothesis ( \( H_A \) )**:
   The alternative hypothesis would test whether the win rate differs from 0.03 (either higher or lower), so:
   \[
   H_A: p \neq 0.03
   \]

In summary, the hypotheses are:
- \( H_0: p = 0.03 \)
- \( H_A: p \neq 0.03 \)

Would you like further details on hypothesis testing, or do you have any questions about this setup?

### Related Questions
1. What is a proportion, and how does it differ from a mean?
2. How would the hypotheses change if the casino was only concerned with verifying if the win rate is lower than 0.03?
3. How would one calculate the test statistic if sample data were provided?
4. What is the significance level, and how does it affect hypothesis testing?
5. How does sample size influence the power of a hypothesis test?

### Tip:
In hypothesis testing, clearly defining the parameter and hypotheses before gathering data helps prevent bias and ensures that conclusions are based solely on statistical evidence.

A casino wants to know if their slot machine really delivers the 3 in 100 win rate that it claims.

Understand how to set up a hypothesis test to verify a slot machine's win rate claim of 3 in 100. This example demonstrates hypothesis testing for proportions, suitable for high school students and those learning about statistical tests.

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