The test statistic of z = -2.13 is obtained when testing the claim that p< 0.43. a. Using a significance level of a= 0.10, find the critical value(s). b. Should we reject Ho or should we fail to reject Ho?

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### Hypothesis Testing Using z-Statistic

**The Scenario:**
The test statistic of \( z = -2.13 \) is obtained when testing the claim that \( p < 0.43 \).

**Steps:**
a. Using a significance level of \( \alpha = 0.10 \), find the critical value(s).  
b. Should we reject \( H_0 \) or should we fail to reject \( H_0 \)?

**Resources:**
You can find the critical values by consulting the standard normal distribution table. Here are the links:
- [Page 1 of the standard normal distribution table](#)
- [Page 2 of the standard normal distribution table](#)

**Solution:**

1. **Finding the Critical Value(s):**  
   a. The critical value(s) is/are \( z = \_\_\_\_\_\_ \).  
   (Round to two decimal places as needed. Use a comma to separate answers as needed.)

2. **Decision Rule:**
   b. Using the critical value found, decide whether to reject \( H_0 \) or fail to reject \( H_0 \).

### Explanation of Diagrams (If Available):
Please refer to the standard normal distribution tables to find the appropriate critical z-value. The significance level \( \alpha = 0.10 \) corresponds to a critical value for a one-tailed test. Normally, in such a case, consult the left-tail of the z-distribution.

### How to Use the Standard Normal Distribution Table:
1. Locate the significance level (e.g., 0.10) in the table.
2. Find the corresponding z-value.
3. Compare the test statistic \( z = -2.13 \) with the critical z-value to determine if \( H_0 \) should be rejected.

By consulting the standard normal distribution table, you can complete parts a. and b., thus enabling the decision-making process for the hypothesis based on the given test statistic.
Transcribed Image Text:### Hypothesis Testing Using z-Statistic **The Scenario:** The test statistic of \( z = -2.13 \) is obtained when testing the claim that \( p < 0.43 \). **Steps:** a. Using a significance level of \( \alpha = 0.10 \), find the critical value(s). b. Should we reject \( H_0 \) or should we fail to reject \( H_0 \)? **Resources:** You can find the critical values by consulting the standard normal distribution table. Here are the links: - [Page 1 of the standard normal distribution table](#) - [Page 2 of the standard normal distribution table](#) **Solution:** 1. **Finding the Critical Value(s):** a. The critical value(s) is/are \( z = \_\_\_\_\_\_ \). (Round to two decimal places as needed. Use a comma to separate answers as needed.) 2. **Decision Rule:** b. Using the critical value found, decide whether to reject \( H_0 \) or fail to reject \( H_0 \). ### Explanation of Diagrams (If Available): Please refer to the standard normal distribution tables to find the appropriate critical z-value. The significance level \( \alpha = 0.10 \) corresponds to a critical value for a one-tailed test. Normally, in such a case, consult the left-tail of the z-distribution. ### How to Use the Standard Normal Distribution Table: 1. Locate the significance level (e.g., 0.10) in the table. 2. Find the corresponding z-value. 3. Compare the test statistic \( z = -2.13 \) with the critical z-value to determine if \( H_0 \) should be rejected. By consulting the standard normal distribution table, you can complete parts a. and b., thus enabling the decision-making process for the hypothesis based on the given test statistic.
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