Sample 1 n1 = 20 x₁ = = 22.7 S₁ = 2.6 $1 Sample 2 72 = 30 x₂ = 20.1 $₂ = 4.4
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
![### Independent Random Samples and Confidence Intervals
**Instructions**: You may need to use the appropriate appendix table or technology to answer this question.
The following results are for independent random samples taken from two populations.
#### Table of Results
| Sample 1 | Sample 2 |
|-------------------------|-------------------------|
| \( n_1 = 20 \) | \( n_2 = 30 \) |
| \( \overline{X}_1 = 22.7 \) | \( \overline{X}_2 = 20.1 \) |
| \( s_1 = 2.6 \) | \( s_2 = 4.4 \) |
### Questions
**(a)** What is the point estimate of the difference between the two population means? (Use \( \overline{X}_1 - \overline{X}_2 \)).
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(b)** What is the degrees of freedom for the \( t \) distribution? (Round your answer down to the nearest integer.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(c)** At 95% confidence, what is the margin of error? (Round your answer to one decimal place.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(d)** What is the 95% confidence interval for the difference between the two population means? (Use \( \overline{X}_1 - \overline{X}_2 \)). Round your answers to one decimal place.)
\[ \boxed{\ \ \ \ \ \ \ \ } \ \text{to} \ \boxed{\ \ \ \ \ \ \ \ } \]
### Detailed Explanation of the Table
The table provides statistical data for two separate samples.
- **Sample 1**:
- \( n_1 = 20 \): The sample size is 20.
- \( \overline{X}_1 = 22.7 \): The sample mean is 22.7.
- \( s_1 = 2.6 \): The sample standard deviation is 2.6.
- **Sample 2**:
- \( n_2 = 30 \): The sample size is 30.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98fd5880-bd7f-4b90-9f43-35abbd9a1544%2F323de376-765e-4216-b9ea-54f9b192292b%2Fkkx4zy_processed.png&w=3840&q=75)
Transcribed Image Text:### Independent Random Samples and Confidence Intervals
**Instructions**: You may need to use the appropriate appendix table or technology to answer this question.
The following results are for independent random samples taken from two populations.
#### Table of Results
| Sample 1 | Sample 2 |
|-------------------------|-------------------------|
| \( n_1 = 20 \) | \( n_2 = 30 \) |
| \( \overline{X}_1 = 22.7 \) | \( \overline{X}_2 = 20.1 \) |
| \( s_1 = 2.6 \) | \( s_2 = 4.4 \) |
### Questions
**(a)** What is the point estimate of the difference between the two population means? (Use \( \overline{X}_1 - \overline{X}_2 \)).
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(b)** What is the degrees of freedom for the \( t \) distribution? (Round your answer down to the nearest integer.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(c)** At 95% confidence, what is the margin of error? (Round your answer to one decimal place.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ } \]
**(d)** What is the 95% confidence interval for the difference between the two population means? (Use \( \overline{X}_1 - \overline{X}_2 \)). Round your answers to one decimal place.)
\[ \boxed{\ \ \ \ \ \ \ \ } \ \text{to} \ \boxed{\ \ \ \ \ \ \ \ } \]
### Detailed Explanation of the Table
The table provides statistical data for two separate samples.
- **Sample 1**:
- \( n_1 = 20 \): The sample size is 20.
- \( \overline{X}_1 = 22.7 \): The sample mean is 22.7.
- \( s_1 = 2.6 \): The sample standard deviation is 2.6.
- **Sample 2**:
- \( n_2 = 30 \): The sample size is 30.
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 with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman