1. **State the problem:** We want to test the claim that the mean wait time at the Space Mountain ride is 49 minutes.
2. **Null hypothesis (H0):** This is the statement that there is no effect or no difference. It is usually a statement of equality.
$$H_0: \mu = 49$$
This means the population mean wait time is 49 minutes.
3. **Alternative hypothesis (H1):** This is what we want to test against the null hypothesis. It represents a difference or effect.
Since the problem states a two-tailed test (mean not equal to 49), the alternative hypothesis is:
$$H_1: \mu \neq 49$$
4. **Explanation:**
- The null hypothesis assumes the average wait time is exactly 49 minutes.
- The alternative hypothesis assumes the average wait time is different from 49 minutes (could be less or more).
This setup is typical for a two-tailed hypothesis test where we check if the mean differs from a specific value.
Final answers:
- Null hypothesis: $H_0: \mu = 49$
- Alternative hypothesis: $H_1: \mu \neq 49$
Hypothesis Test D88542
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.