Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.98, x= 13.3, s=0.88, n= 12 ..... (Round to one decimal place as needed.)
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.98, x= 13.3, s=0.88, n= 12 ..... (Round to one decimal place as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Answer question
![**Constructing Confidence Intervals Using the t-Distribution**
To calculate the confidence interval for the population mean \( \mu \) using the t-distribution, follow these steps. In this example, assume the population is normally distributed.
Given:
- Confidence level (\( c \)): 0.98
- Sample mean (\( \bar{x} \)): 13.3
- Sample standard deviation (\( s \)): 0.88
- Sample size (\( n \)): 12
**Steps:**
1. **Determine the degrees of freedom**:
\[
\text{Degrees of Freedom} = n - 1 = 12 - 1 = 11
\]
2. **Find the critical value (\( t^* \)):**
Use a t-distribution table or calculator to find the critical t-value corresponding to the confidence level of 0.98 and 11 degrees of freedom.
3. **Calculate the margin of error (\( E \))**:
\[
E = t^* \times \frac{s}{\sqrt{n}}
\]
4. **Determine the confidence interval**:
\[
\text{Confidence Interval} = \left( \bar{x} - E, \bar{x} + E \right)
\]
(Round to one decimal place as needed.)
**Further Exploration:**
- **Help Me Solve This**: This option guides you through each calculation step-by-step.
- **View an Example**: Provides a similar problem with a detailed solution.
- **Get More Help**: Links to additional resources for understanding confidence intervals.
**Interactive Checkbox**: Provides an option to toggle between hiding and displaying the calculated confidence interval.
(Note: There are no graphs or diagrams in this content. The emphasis is on understanding and computing the confidence interval using statistical formulas.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7226e99-cda6-474c-a507-35a166b04cf3%2F90297f82-37f6-465f-bd5a-578778ed0906%2F9u8uext_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing Confidence Intervals Using the t-Distribution**
To calculate the confidence interval for the population mean \( \mu \) using the t-distribution, follow these steps. In this example, assume the population is normally distributed.
Given:
- Confidence level (\( c \)): 0.98
- Sample mean (\( \bar{x} \)): 13.3
- Sample standard deviation (\( s \)): 0.88
- Sample size (\( n \)): 12
**Steps:**
1. **Determine the degrees of freedom**:
\[
\text{Degrees of Freedom} = n - 1 = 12 - 1 = 11
\]
2. **Find the critical value (\( t^* \)):**
Use a t-distribution table or calculator to find the critical t-value corresponding to the confidence level of 0.98 and 11 degrees of freedom.
3. **Calculate the margin of error (\( E \))**:
\[
E = t^* \times \frac{s}{\sqrt{n}}
\]
4. **Determine the confidence interval**:
\[
\text{Confidence Interval} = \left( \bar{x} - E, \bar{x} + E \right)
\]
(Round to one decimal place as needed.)
**Further Exploration:**
- **Help Me Solve This**: This option guides you through each calculation step-by-step.
- **View an Example**: Provides a similar problem with a detailed solution.
- **Get More Help**: Links to additional resources for understanding confidence intervals.
**Interactive Checkbox**: Provides an option to toggle between hiding and displaying the calculated confidence interval.
(Note: There are no graphs or diagrams in this content. The emphasis is on understanding and computing the confidence interval using statistical formulas.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON