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It looks like you are working on a hypothesis testing problem involving a **two-tailed z-test** using the **p-value method**. Here's a breakdown of the problem based on the image:

1. **Step 1: One-tailed or Two-tailed Test**
   - You selected a **two-tailed test**, which means the alternative hypothesis is non-directional (i.e., it tests for a difference in either direction).

2. **Step 2: Test Statistic (z-value)**
   - The z-value provided is **-2.108** (on both sides since it's symmetrical for two-tailed tests). This z-score helps us determine how extreme the sample statistic is compared to the population mean.

3. **Step 3: Shading the p-value Area**
   - The area under the curve for each tail is **0.0175**, meaning that the combined area for both tails (p-value) will be **2 × 0.0175 = 0.035**.

4. **Step 4: Enter p-value**
   - The p-value calculated is **0.035**. This is the probability of observing a test statistic as extreme as -2.108 under the null hypothesis.

### Explanation:
- For a **two-tailed test**, you test both extremes (positive and negative z-values).
- The area under the curve represents the **p-value**, which helps you determine whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), you reject the null hypothesis.

Would you like more details on this topic or specific steps explained further?

Here are 5 related questions to explore:

1. How do you decide between a one-tailed and a two-tailed test?
2. What are the critical values for a two-tailed z-test at a significance level of 0.05?
3. How does the p-value method compare to the critical value method?
4. Why is it important to round the test statistic to three decimal places?
5. How do you interpret the p-value in the context of hypothesis testing?

**Tip**: Always ensure you understand the difference between one-tailed and two-tailed tests, as this affects the calculation of the p-value and the conclusion drawn from the test.

The user is working on a two-tailed z-test using the p-value method with a test statistic of z = -2.108.

Understand how to perform a two-tailed z-test using the p-value method with a z-score of -2.108. Learn the step-by-step process of calculating the p-value and interpreting the results in hypothesis testing. Suitable for college-level statistics students.

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