(a) Consider a t distribution with 30 degrees of freedom. Compute P(-1.46
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![### Statistical Problem Set
#### Problem 1: t Distribution and Degrees of Freedom
**(a)** Consider a **t distribution** with **30 degrees of freedom**. Compute \( P( -1.46 < t < 1.46 ) \). Round your answer to at least three decimal places.
\[ P( -1.46 < t < 1.46 ) = \boxed{} \]
**(b)** Consider a **t distribution** with **28 degrees of freedom**. Find the value of \( c \) such that \( P( t \geq c ) = 0.10 \). Round your answer to at least three decimal places.
\[ c = \boxed{} \]
### Explanation:
- **t Distribution**: Also known as Student's t-distribution, it is defined by the degrees of freedom. It is used especially when the sample size is small and the population standard deviation is unknown.
- **Degrees of Freedom**: Typically denoted as \( \text{df} \), this is the number of values in the final calculation of a statistic that are free to vary.
In this problem, you are provided specific values for degrees of freedom and are required to find probabilities and critical values associated with the t distribution.
### Diagrams
While the text lacks actual diagrams, we can conceptualize the following:
1. **Graph for Part (a)**:
- It would depict a standard t-distribution curve with 30 degrees of freedom.
- The region between -1.46 and 1.46 under the curve would be highlighted to show the range for which the probability is being computed.
2. **Graph for Part (b)**:
- It would depict a t-distribution curve with 28 degrees of freedom.
- The area to the right of the value \( c \) would be shaded to indicate that \( P( t \geq c ) \) corresponds to 0.10 or 10%.
### Important Notes
- Knowing how to use t-tables or statistical software can be crucial in solving these problems.
- The results are typically more accurate when computed using these tools, as they provide exact values for the given degrees of freedom.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50a93c10-85d4-41d2-a577-62aadf58513c%2F30a80462-8895-4e0d-84eb-cb98c8c07c05%2Fc47r5mc_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Problem Set
#### Problem 1: t Distribution and Degrees of Freedom
**(a)** Consider a **t distribution** with **30 degrees of freedom**. Compute \( P( -1.46 < t < 1.46 ) \). Round your answer to at least three decimal places.
\[ P( -1.46 < t < 1.46 ) = \boxed{} \]
**(b)** Consider a **t distribution** with **28 degrees of freedom**. Find the value of \( c \) such that \( P( t \geq c ) = 0.10 \). Round your answer to at least three decimal places.
\[ c = \boxed{} \]
### Explanation:
- **t Distribution**: Also known as Student's t-distribution, it is defined by the degrees of freedom. It is used especially when the sample size is small and the population standard deviation is unknown.
- **Degrees of Freedom**: Typically denoted as \( \text{df} \), this is the number of values in the final calculation of a statistic that are free to vary.
In this problem, you are provided specific values for degrees of freedom and are required to find probabilities and critical values associated with the t distribution.
### Diagrams
While the text lacks actual diagrams, we can conceptualize the following:
1. **Graph for Part (a)**:
- It would depict a standard t-distribution curve with 30 degrees of freedom.
- The region between -1.46 and 1.46 under the curve would be highlighted to show the range for which the probability is being computed.
2. **Graph for Part (b)**:
- It would depict a t-distribution curve with 28 degrees of freedom.
- The area to the right of the value \( c \) would be shaded to indicate that \( P( t \geq c ) \) corresponds to 0.10 or 10%.
### Important Notes
- Knowing how to use t-tables or statistical software can be crucial in solving these problems.
- The results are typically more accurate when computed using these tools, as they provide exact values for the given degrees of freedom.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
