**Finding the Critical Value for a Given Confidence Level**To calculate the critical value $ z_{\alpha/2} $ associated with a specific confidence level, follow these steps. Here, we are given a confidence level of 82%.1. **Understanding Confidence Level**: The confidence level represents the probability that the true parameter of interest falls within the confidence interval. An 82% confidence level means that we are 82% confident that the interval will capture the true parameter.2. **Calculate Alpha ($ \alpha $)**: \[ \alpha = 1 - \text{Confidence Level} = 1 - 0.82 = 0.18 \] 3. **Divide Alpha by 2**: \[ \alpha/2 = 0.18/2 = 0.09 \]4. **Find $ z_{\alpha/2} $**: Use a standard normal distribution table (z-table) or a statistical calculator to find the z-score that corresponds to the cumulative probability of $ 1 - \alpha/2 = 0.91 $. - The critical value $ z_{\alpha/2} $ will give you the z-score where 91% of the distribution is to the left, and 9% is to the right in a standard normal distribution.5. **Round the Result**: Once the z-score is identified, round it to two decimal places as required.\[ z_{\alpha/2} = \boxed{[Enter the rounded value here]} \]**Note**: When looking up the z-score, make sure your z-table or calculator input is accurate. This exercise helps in constructing confidence intervals and understanding hypothesis testing in statistics.

Solution: The confidence level is given to be 82%. Confidence level: C= 0.82 α=1-C = 1-0.82 = 0.18…

Answered: Find the critical value za/2 that…

Find the critical value za/2 that corresponds to the given confidence level. 82% 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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

**Finding the Critical Value for a Given Confidence Level**

To calculate the critical value $ z_{\alpha/2} $ associated with a specific confidence level, follow these steps. Here, we are given a confidence level of 82%.

1. **Understanding Confidence Level**: The confidence level represents the probability that the true parameter of interest falls within the confidence interval. An 82% confidence level means that we are 82% confident that the interval will capture the true parameter.

2. **Calculate Alpha ($ \alpha $)**:
\[
\alpha = 1 - \text{Confidence Level} = 1 - 0.82 = 0.18
\]

3. **Divide Alpha by 2**:
\[
\alpha/2 = 0.18/2 = 0.09
\]

4. **Find $ z_{\alpha/2} $**: Use a standard normal distribution table (z-table) or a statistical calculator to find the z-score that corresponds to the cumulative probability of $ 1 - \alpha/2 = 0.91 $.

- The critical value $ z_{\alpha/2} $ will give you the z-score where 91% of the distribution is to the left, and 9% is to the right in a standard normal distribution.

5. **Round the Result**: Once the z-score is identified, round it to two decimal places as required.

\[ z_{\alpha/2} = \boxed{[Enter the rounded value here]} \]

**Note**: When looking up the z-score, make sure your z-table or calculator input is accurate. This exercise helps in constructing confidence intervals and understanding hypothesis testing in statistics.

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