A coin-operated drink machine was designed to discharge a mean of 6 ounces of coffee per cup. Suppose that we want to carry out a hypothesis test to see if the true mean discharge differs from . State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.

In this case, the hypothesis test is aimed at determining whether the true mean amount of coffee dispensed by the machine differs from the design specification of 6 ounces. The null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)) would be set up as follows:

- **Null Hypothesis (\(H_0\))**: The mean amount of coffee dispensed by the machine is equal to 6 ounces.
  \[
  H_0: \mu = 6 \text{ ounces}
  \]

- **Alternative Hypothesis (\(H_1\))**: The mean amount of coffee dispensed by the machine is different from 6 ounces.
  \[
  H_1: \mu \neq 6 \text{ ounces}
  \]

This is a two-tailed test because the alternative hypothesis considers both possibilities: that the mean could be either greater than or less than 6 ounces.

Would you like more details or have any questions?

Here are 8 related questions that might interest you:

1. What are the steps involved in conducting a two-tailed hypothesis test?
2. How do you determine the critical value(s) for a two-tailed test?
3. What role does the significance level (\(\alpha\)) play in hypothesis testing?
4. How would you calculate the p-value for a two-tailed test?
5. What is the difference between a z-test and a t-test in hypothesis testing?
6. How can you check if the coffee machine’s discharge follows a normal distribution?
7. What happens if the assumptions for the hypothesis test are violated?
8. How would you interpret the results if the null hypothesis is not rejected?

**Tip:** In a two-tailed test, the critical region for rejection of the null hypothesis is split between both ends of the distribution, making it important to accurately calculate the critical values or p-values for both tails.

Understand hypothesis testing to determine if a coin-operated drink machine's true mean discharge differs from the specified 6 ounces. Learn about the null and alternative hypotheses, two-tailed tests, and interpreting results.

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