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.
H1
H0:

In hypothesis testing, we set up a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_1\)) to test a claim about a population parameter.

### Null Hypothesis (\(H_0\)):
The null hypothesis represents the statement of no effect or no difference. In this case, it would state that the true mean discharge of the machine is equal to 8 ounces.

\[
H_0: \mu = 8 \, \text{ounces}
\]

### Alternative Hypothesis (\(H_1\)):
The alternative hypothesis represents what we are trying to find evidence for. Here, it would state that the true mean discharge of the machine is different from 8 ounces. Since we are checking if it "differs," this is a two-tailed test.

\[
H_1: \mu \neq 8 \, \text{ounces}
\]

So, the hypotheses for this test are:

\[
H_0: \mu = 8 \, \text{ounces}
\]
\[
H_1: \mu \neq 8 \, \text{ounces}
\]

Do you want more details, or have any questions?

Here are five related questions to explore further:
1. How would you determine the significance level for this hypothesis test?
2. What type of test statistic would be appropriate for this hypothesis test?
3. How do you calculate the p-value for this test, and what does it represent?
4. What are Type I and Type II errors in the context of this hypothesis test?
5. How would the test procedure differ if we were interested in whether the mean discharge is less than 8 ounces?

**Tip:** Always specify whether your hypothesis test is one-tailed or two-tailed before conducting the test, as it impacts the interpretation of the p-value.

Explore hypothesis testing to determine if the mean discharge of a coin-operated drink machine differs from 8 ounces. Learn about null and alternative hypotheses, significance levels, test statistics, and p-values.

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