Consider a normal population distribution with the value of a known. LUSE 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 + 1.470/√n? (Round your answer to one decimal place.) ²a/2 % (c) What value of Za/2 in the CI formula below results in a confidence level of 99.7% ? (Round your answer to two decimal places.) ²a/2 √ ₁ X + 2₁ ₂X+²₁/2¹/7) (d) Answer the question posed in part (c) for a confidence level of 70%. (Round your answer to two decimal places.) ²a/2=
Consider a normal population distribution with the value of a known. LUSE 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 + 1.470/√n? (Round your answer to one decimal place.) ²a/2 % (c) What value of Za/2 in the CI formula below results in a confidence level of 99.7% ? (Round your answer to two decimal places.) ²a/2 √ ₁ X + 2₁ ₂X+²₁/2¹/7) (d) Answer the question posed in part (c) for a confidence level of 70%. (Round your answer to two decimal places.) ²a/2=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Confidence Intervals and z-values
Consider a normal population distribution with the value of σ known.
#### Exercises:
**(a) What is the confidence level for the interval \(\bar{x} \pm 2.88 \frac{\sigma}{\sqrt{n}}\)? (Round your answer to one decimal place.)**
\[ \_\_\_\_\_\_\_ \%\]
**(b) What is the confidence level for the interval \(\bar{x} \pm 1.47 \frac{\sigma}{\sqrt{n}}\)? (Round your answer to one decimal place.)**
\[ \_\_\_\_\_\_\_ \%\]
**(c) 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.)**
\[
\left( \bar{x} - z_{\alpha/2} \frac{\sigma}{\sqrt{n}}, \bar{x} + z_{\alpha/2} \frac{\sigma}{\sqrt{n}} \right)
\]
\[ z_{\alpha/2} = \_\_\_\_\_\_\_\_\_ \]
**(d) Answer the question posed in part (c) for a confidence level of 70%. (Round your answer to two decimal places.)**
\[ z_{\alpha/2} = \_\_\_\_\_\_\_\_\_ \]
---
### Explanation of Diagrams
- **Confidence Intervals Formula**: Represents the range within which the population parameter is expected to lie.
- **z-value (or z-score)**: Indicates the number of standard deviations a point is from the mean.
Each part requires identifying confidence levels or corresponding z-values, essential concepts in inferential statistics.
To solve these problems, you may need to refer to a z-table or use statistical software to find the corresponding values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb989860-4d1c-4fb5-9e6b-42a4528dce9c%2F4575459c-89cd-47fe-9935-1d0b544421e9%2Fahqqwm5ak_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Intervals and z-values
Consider a normal population distribution with the value of σ known.
#### Exercises:
**(a) What is the confidence level for the interval \(\bar{x} \pm 2.88 \frac{\sigma}{\sqrt{n}}\)? (Round your answer to one decimal place.)**
\[ \_\_\_\_\_\_\_ \%\]
**(b) What is the confidence level for the interval \(\bar{x} \pm 1.47 \frac{\sigma}{\sqrt{n}}\)? (Round your answer to one decimal place.)**
\[ \_\_\_\_\_\_\_ \%\]
**(c) 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.)**
\[
\left( \bar{x} - z_{\alpha/2} \frac{\sigma}{\sqrt{n}}, \bar{x} + z_{\alpha/2} \frac{\sigma}{\sqrt{n}} \right)
\]
\[ z_{\alpha/2} = \_\_\_\_\_\_\_\_\_ \]
**(d) Answer the question posed in part (c) for a confidence level of 70%. (Round your answer to two decimal places.)**
\[ z_{\alpha/2} = \_\_\_\_\_\_\_\_\_ \]
---
### Explanation of Diagrams
- **Confidence Intervals Formula**: Represents the range within which the population parameter is expected to lie.
- **z-value (or z-score)**: Indicates the number of standard deviations a point is from the mean.
Each part requires identifying confidence levels or corresponding z-values, essential concepts in inferential statistics.
To solve these problems, you may need to refer to a z-table or use statistical software to find the corresponding values.
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