(c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) X (d) What is the 95% confidence interval for the difference between the two population means? (Use x₁ - x₂. Round your answers to one decimal place.) to
(c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) X (d) What is the 95% confidence interval for the difference between the two population means? (Use x₁ - x₂. Round your answers to one decimal place.) to
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I need help finding part c and d
![### Understanding Statistical Differences: An Example
In this exercise, we explore the statistical analysis of two independent random samples from different populations.
#### Sample Descriptions
- **Sample 1**:
- Sample Size (\(n_1\)): 20
- Sample Mean (\(\bar{x}_1\)): 22.9
- Sample Standard Deviation (\(s_1\)): 2.1
- **Sample 2**:
- Sample Size (\(n_2\)): 30
- Sample Mean (\(\bar{x}_2\)): 20.1
- Sample Standard Deviation (\(s_2\)): 4.8
#### Analysis Tasks
**(a) Point Estimate of the Difference Between Population Means**
- The point estimate is calculated as the difference between the two sample means:
\[
\text{Point Estimate} = \bar{x}_1 - \bar{x}_2 = 22.9 - 20.1 = 2.8
\]
**(b) Degrees of Freedom for the t Distribution**
- To estimate the degrees of freedom, we round down to the nearest integer, resulting in:
\[
\text{Degrees of Freedom} = 42
\]
**(c) Margin of Error at 95% Confidence**
- Calculate using statistical techniques and round your answer to one decimal place.
**(d) 95% Confidence Interval for the Difference Between Population Means**
- Using the point estimate, calculate the interval and express it to one decimal place.
### Conclusion
This exercise demonstrates how to assess statistical differences between two independent groups using point estimates, degrees of freedom, and confidence intervals.
This type of analysis is essential in various fields, such as science and business, for making informed decisions based on sample data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc3d35d9-d391-4981-9679-d316add0bad2%2F5e331b8b-1041-4f65-a5e8-8cd08dd48416%2Ff0xkj4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Statistical Differences: An Example
In this exercise, we explore the statistical analysis of two independent random samples from different populations.
#### Sample Descriptions
- **Sample 1**:
- Sample Size (\(n_1\)): 20
- Sample Mean (\(\bar{x}_1\)): 22.9
- Sample Standard Deviation (\(s_1\)): 2.1
- **Sample 2**:
- Sample Size (\(n_2\)): 30
- Sample Mean (\(\bar{x}_2\)): 20.1
- Sample Standard Deviation (\(s_2\)): 4.8
#### Analysis Tasks
**(a) Point Estimate of the Difference Between Population Means**
- The point estimate is calculated as the difference between the two sample means:
\[
\text{Point Estimate} = \bar{x}_1 - \bar{x}_2 = 22.9 - 20.1 = 2.8
\]
**(b) Degrees of Freedom for the t Distribution**
- To estimate the degrees of freedom, we round down to the nearest integer, resulting in:
\[
\text{Degrees of Freedom} = 42
\]
**(c) Margin of Error at 95% Confidence**
- Calculate using statistical techniques and round your answer to one decimal place.
**(d) 95% Confidence Interval for the Difference Between Population Means**
- Using the point estimate, calculate the interval and express it to one decimal place.
### Conclusion
This exercise demonstrates how to assess statistical differences between two independent groups using point estimates, degrees of freedom, and confidence intervals.
This type of analysis is essential in various fields, such as science and business, for making informed decisions based on sample data.
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