Find the critical value z/2 that corresponds to the given confidence leve 97% Za/2= (Round to two decimal places as needed.)
Find the critical value z/2 that corresponds to the given confidence leve 97% Za/2= (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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![**Educational Content: Finding Critical Values for Confidence Levels**
In the study of statistics, finding the critical value for a specified confidence level is a common task, particularly when constructing confidence intervals for population parameters.
---
**Task:**
Find the critical value \( z_{\alpha/2} \) that corresponds to the given confidence level.
**Given Confidence Level:**
97%
\[
z_{\alpha/2} = \, \_ \, \_ \, (Round \, to \, two \, decimal \, places \, as \, needed.)
\]
---
To find the critical value \( z_{\alpha/2} \):
1. **Identify the Confidence Level**: The confidence level given here is 97%. This means that we are looking to capture 97% of the data under the standard normal distribution curve, leaving 3% in the tails (1.5% in each tail since it’s a two-tailed distribution).
2. **Compute \(\alpha\)**: \(\alpha = 1 - 0.97 = 0.03\).
3. **Divide \(\alpha\) by 2**: \(\frac{\alpha}{2} = \frac{0.03}{2} = 0.015\).
4. **Find the Critical Value**: Using a standard normal distribution table, or statistical software, find the z-value such that the area to the right is 0.015. This provides the critical value \( z_{\alpha/2} \).
By rounding this value to two decimal places, you will obtain the critical z-value for constructing a 97% confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2042fb1-363a-4ac8-9b5e-36efb4689de7%2Fb6a0953c-7717-404c-8e04-6e94837b9043%2Fmdwwu3w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Finding Critical Values for Confidence Levels**
In the study of statistics, finding the critical value for a specified confidence level is a common task, particularly when constructing confidence intervals for population parameters.
---
**Task:**
Find the critical value \( z_{\alpha/2} \) that corresponds to the given confidence level.
**Given Confidence Level:**
97%
\[
z_{\alpha/2} = \, \_ \, \_ \, (Round \, to \, two \, decimal \, places \, as \, needed.)
\]
---
To find the critical value \( z_{\alpha/2} \):
1. **Identify the Confidence Level**: The confidence level given here is 97%. This means that we are looking to capture 97% of the data under the standard normal distribution curve, leaving 3% in the tails (1.5% in each tail since it’s a two-tailed distribution).
2. **Compute \(\alpha\)**: \(\alpha = 1 - 0.97 = 0.03\).
3. **Divide \(\alpha\) by 2**: \(\frac{\alpha}{2} = \frac{0.03}{2} = 0.015\).
4. **Find the Critical Value**: Using a standard normal distribution table, or statistical software, find the z-value such that the area to the right is 0.015. This provides the critical value \( z_{\alpha/2} \).
By rounding this value to two decimal places, you will obtain the critical z-value for constructing a 97% confidence interval.
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