Consider a normal population distribution with the value of a known. USE SALT (a) What is the confidence level for the interval x ± 2.880/√n? (Round your answer to one decimal place.) % (b) What is the confidence level for the interval x ± 1.450/√n? (Round your answer to one decimal place.) % (c) What value of z in the CI formula below results in a confidence level of 99.7%? (Round your answer to two decimal places.) a/2 O - Zal x + Za/2 FF) n Za/2 (d) Answer the question posed in part (c) for a confidence level of 62%. (Round your answer to two decimal places.) Za/2

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Q10

### Understanding Confidence Intervals

Consider a normal population distribution with a known value of \(\sigma\).

#### Instructions:

1. **Use Salt Button:**
   - Click the **Use Salt** button for additional assistance or tools.

#### Exercise Questions:

(a) **Confidence Level for Interval \( \bar{x} \pm 2.88\frac{\sigma}{\sqrt{n}} \):**
   - Determine the confidence level for the interval \( \bar{x} \pm 2.88\frac{\sigma}{\sqrt{n}} \).
   - Round your answer to one decimal place.
   
   **Answer:**
   \[ \_\_\_\_ \% \]

(b) **Confidence Level for Interval \( \bar{x} \pm 1.45\frac{\sigma}{\sqrt{n}} \):**
   - Determine the confidence level for the interval \( \bar{x} \pm 1.45\frac{\sigma}{\sqrt{n}} \).
   - Round your answer to one decimal place.
   
   **Answer:**
   \[ \_\_\_\_ \% \]

(c) **Value of \( z_{\alpha/2} \) for a Confidence Level of 99.7%:**
   - What value of \( z_{\alpha/2} \) in the CI formula below results in a confidence level of 99.7%?
   - Round your answer to two decimal places.
   
   \[
   \left( \bar{x} - z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}, \bar{x} + z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}} \right)
   \]

   **Answer:**
   \[ z_{\alpha/2} = \_\_\_\_ \]

(d) **Value of \( z_{\alpha/2} \) for a Confidence Level of 62%:**
   - Answer the question posed in part (c) for a confidence level of 62%.
   - Round your answer to two decimal places.
   
   **Answer:**
   \[ z_{\alpha/2} = \_\_\_\_ \]
Transcribed Image Text:### Understanding Confidence Intervals Consider a normal population distribution with a known value of \(\sigma\). #### Instructions: 1. **Use Salt Button:** - Click the **Use Salt** button for additional assistance or tools. #### Exercise Questions: (a) **Confidence Level for Interval \( \bar{x} \pm 2.88\frac{\sigma}{\sqrt{n}} \):** - Determine the confidence level for the interval \( \bar{x} \pm 2.88\frac{\sigma}{\sqrt{n}} \). - Round your answer to one decimal place. **Answer:** \[ \_\_\_\_ \% \] (b) **Confidence Level for Interval \( \bar{x} \pm 1.45\frac{\sigma}{\sqrt{n}} \):** - Determine the confidence level for the interval \( \bar{x} \pm 1.45\frac{\sigma}{\sqrt{n}} \). - Round your answer to one decimal place. **Answer:** \[ \_\_\_\_ \% \] (c) **Value of \( z_{\alpha/2} \) for a Confidence Level of 99.7%:** - What value of \( z_{\alpha/2} \) in the CI formula below results in a confidence level of 99.7%? - Round your answer to two decimal places. \[ \left( \bar{x} - z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}, \bar{x} + z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}} \right) \] **Answer:** \[ z_{\alpha/2} = \_\_\_\_ \] (d) **Value of \( z_{\alpha/2} \) for a Confidence Level of 62%:** - Answer the question posed in part (c) for a confidence level of 62%. - Round your answer to two decimal places. **Answer:** \[ z_{\alpha/2} = \_\_\_\_ \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman