### 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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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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

### 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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