A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. Suppose that we want to carry out a hypothesis test to see if the true mean discharge differs from 8. State the null hypothesis He and the alternative hypothesis H, that we would use for this test.

Ho



The null hypothesis (Ho) and alternative hypothesis (Ha) for this hypothesis test can be stated as follows:

- **Null Hypothesis (Ho):** The true mean discharge of the drink machine is equal to 8 ounces.
  \[
  H_0: \mu = 8
  \]
  
- **Alternative Hypothesis (Ha):** The true mean discharge of the drink machine differs from 8 ounces.
  \[
  H_a: \mu \neq 8
  \]

This is a **two-tailed test**, as the alternative hypothesis checks for any difference (greater than or less than 8 ounces), not just in one direction.

Would you like details on how to proceed with this hypothesis test, or have any questions on hypothesis testing?

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Here are 5 related questions:
1. How do you determine the appropriate significance level (α) for the test?
2. What is the next step after stating the hypotheses in a hypothesis test?
3. How do you compute the test statistic for this hypothesis test?
4. What type of statistical test would be used for this scenario (e.g., t-test, z-test)?
5. How do you interpret the p-value in this context?

**Tip:** Always check if the sample size is large enough and whether the population follows a normal distribution when conducting hypothesis tests.

A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. Suppose that we want to carry out a hypothesis test to see if the true mean discharge differs from 8. State the null hypothesis Ho and the alternative hypothesis Ha that we would use for this test.

Learn how to perform a hypothesis test to determine if the true mean discharge of a drink machine differs from the specified 8 ounces. This problem involves key statistical concepts such as hypothesis testing, population mean, and the use of the Central Limit Theorem. Suitable for undergraduate students.

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