Find the critical value za/2 that corresponds to the given confidence level. 86% Za/2%D Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Critical Value Calculation

#### Problem Statement:
Find the critical value \( z_{\alpha/2} \) that corresponds to the given confidence level.

#### Given:
- **Confidence Level:** 86%

#### Required:
- Determine the value of \( z_{\alpha/2} \)
- Round the result to two decimal places as needed.

#### Solution:
To find this critical value, use the following steps:
1. **Determine the Alpha Level**: 
   \[
   \alpha = 1 - \text{Confidence Level} = 1 - 0.86 = 0.14
   \]
   
2. **Divide Alpha by 2**:
   \[
   \alpha/2 = 0.14 / 2 = 0.07
   \]

3. **Find the Complementary Probability**:
   \[
   1 - 0.07 = 0.93
   \]
   
4. **Use the Z-table**:
   Find the z-score that corresponds to 0.93 in the standard normal distribution table.

5. **Determine \( z_{\alpha/2} \)**:
   - You will find that the value of \( z_{\alpha/2} \) is approximately 1.48 after consulting the Z-table.
   
Hence, the answer is:
\[
z_{\alpha/2} = 1.48
\]

---

This critical value is essential in determining confidence intervals in statistics. Ensure to accurately locate the z-score corresponding to the cumulative probability from the Z-table to solve similar problems correctly.
Transcribed Image Text:### Critical Value Calculation #### Problem Statement: Find the critical value \( z_{\alpha/2} \) that corresponds to the given confidence level. #### Given: - **Confidence Level:** 86% #### Required: - Determine the value of \( z_{\alpha/2} \) - Round the result to two decimal places as needed. #### Solution: To find this critical value, use the following steps: 1. **Determine the Alpha Level**: \[ \alpha = 1 - \text{Confidence Level} = 1 - 0.86 = 0.14 \] 2. **Divide Alpha by 2**: \[ \alpha/2 = 0.14 / 2 = 0.07 \] 3. **Find the Complementary Probability**: \[ 1 - 0.07 = 0.93 \] 4. **Use the Z-table**: Find the z-score that corresponds to 0.93 in the standard normal distribution table. 5. **Determine \( z_{\alpha/2} \)**: - You will find that the value of \( z_{\alpha/2} \) is approximately 1.48 after consulting the Z-table. Hence, the answer is: \[ z_{\alpha/2} = 1.48 \] --- This critical value is essential in determining confidence intervals in statistics. Ensure to accurately locate the z-score corresponding to the cumulative probability from the Z-table to solve similar problems correctly.
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