A brewery claims that the mean amount of beer in their bottles is at least 12 ounces. Determine whether the hypothesis test for this claim is​ left-tailed, right-tailed, or​ two-tailed.

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Part 1

A.

​two-tailed

B.

​left-tailed

C.

​right-tailed

To determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, let's break down the claim:

- The brewery claims that the mean amount of beer in their bottles is **at least 12 ounces**.

This is a hypothesis test problem. Let's define the hypotheses:

- **Null Hypothesis (\( H_0 \))**: The mean amount of beer is at least 12 ounces. Mathematically, \( H_0: \mu \geq 12 \).
- **Alternative Hypothesis (\( H_1 \))**: The mean amount of beer is less than 12 ounces. Mathematically, \( H_1: \mu < 12 \).

Since the alternative hypothesis tests whether the mean is **less than** 12 ounces, this is a **left-tailed** test.

### Answer:
**B. Left-tailed**

Would you like more details about hypothesis testing or have any other questions?

### Related Questions:
1. How do you determine if a test is one-tailed or two-tailed?
2. What is the difference between a left-tailed and right-tailed test?
3. What role does the null hypothesis play in hypothesis testing?
4. How do you calculate the test statistic for hypothesis testing?
5. When should you use a two-tailed test instead of a one-tailed test?
6. What is the significance level in hypothesis testing?
7. How is the p-value interpreted in left-tailed tests?
8. What assumptions need to be satisfied for a valid hypothesis test?

### Tip:
Always align the direction of your alternative hypothesis with the nature of the claim you're testing (less than, greater than, or not equal).

Understand how to determine if a hypothesis test is left-tailed, right-tailed, or two-tailed with an example involving a brewery's claim about the mean amount of beer in bottles. Explore the null and alternative hypotheses, significance levels, and p-values.

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