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.