(b) Find the critical​ value(s) and identify the rejection​ region(s).
Identify the critical​ value(s) for this test.
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​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

To find the critical value(s) and identify the rejection region(s) for this test, we need to use the significance level \(\alpha = 0.05\) for a right-tailed test.

### Step-by-Step Process

1. **Determine the critical value:**

   For a right-tailed test at \(\alpha = 0.05\), we need to find the z-score that corresponds to the area to the right of the critical value being 0.05.

   Using the standard normal (Z) distribution table or a calculator, we find that the critical value \( z_0 \) that leaves 0.05 in the right tail is approximately 1.645.

   \[
   z_0 = 1.645
   \]

2. **Identify the rejection region:**

   The rejection region is the range of values for the test statistic that will lead us to reject the null hypothesis. For a right-tailed test, we reject \( H_0 \) if the test statistic \( z \) is greater than the critical value.

   \[
   \text{Rejection region: } z > 1.645
   \]

### Summary
- **Critical Value**: \( z_0 = 1.645 \)
- **Rejection Region**: \( z > 1.645 \)

Would you like more details or have any questions about the process? Here are some related questions you might find interesting:

1. How do you interpret the critical value in hypothesis testing?
2. What is the difference between critical value and p-value?
3. How does changing the significance level affect the critical value and rejection region?
4. Can you explain why we use the Z-distribution in this context?
5. How would the test change if it were a two-tailed test instead of a one-tailed test?
6. What are the implications of rejecting the null hypothesis in this context?
7. How do you use a standard normal table to find critical values?
8. What are some common mistakes to avoid when identifying rejection regions?

**Tip:** Always ensure you are using the correct critical value for the specific tail of the test (right-tailed, left-tailed, or two-tailed) to avoid incorrect conclusions.

Learn how to find critical values and rejection regions in hypothesis testing using the standard normal distribution. This problem involves determining the critical value for a right-tailed test and identifying the rejection region based on a significance level of α = 0.05. Explore step-by-step solutions and understand the application of the standard normal distribution in statistical hypothesis testing.

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