4. According to those who know, a sample of 360 one year old baby boys in the US had a mean weight of 26.5 pounds. Assume the population standard deviation is or 5.3 pounds. a. Construct a 95% confidence interval for the mean weight of all one-year old baby boys in the M = 262 = 5 M- 0.14 Y b. Based on the confidence interval level above, is it likely that the mean weight of one-year old boys is less than 28 pounds? M = 0.14 = 360 m= DAS X
4. According to those who know, a sample of 360 one year old baby boys in the US had a mean weight of 26.5 pounds. Assume the population standard deviation is or 5.3 pounds. a. Construct a 95% confidence interval for the mean weight of all one-year old baby boys in the M = 262 = 5 M- 0.14 Y b. Based on the confidence interval level above, is it likely that the mean weight of one-year old boys is less than 28 pounds? M = 0.14 = 360 m= DAS X
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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![**Transcription for Educational Use**
---
**Statistics and Probability: Confidence Intervals**
4. According to those who know, a sample of 360 one-year-old baby boys in the US had a mean weight of 26.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.
a. **Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the US.**
- **Calculations and Formulas:**
- M = 26.5
- σ = 5.3
- n = 360
- Confidence Level = 95%
- Use the formula for the confidence interval:
\[
\text{Confidence Interval} = \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right)
\]
- Here, \(\bar{x}\) is the sample mean, z is the z-score corresponding to the 95% confidence level (approximately 1.96), and n is the sample size.
b. **Based on the confidence interval level above, is it likely that the mean weight of all one-year-old boys is less than 28 pounds?**
- **Analysis Consideration:**
- Use the constructed confidence interval to determine if 28 pounds is within this range.
- If 28 pounds is above the upper bound of the interval, it suggests that it is unlikely for the mean weight to be less than 28 pounds.
**Diagrams and Mathematical Notations:**
- The handwritten notes on the paper show sample calculations, such as:
- M = 26.5
- σ = 5.3
- Calculations involving the z-score for a 95% confidence interval.
Note: Ensure that when conducting your own calculations, all steps are clearly shown to maintain accuracy and clarity.
---
This information is intended to help users understand how to construct and interpret confidence intervals for statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ee5d418-4908-4b12-8875-38434e326383%2F56e13d24-0b07-4189-b985-42dd405263ea%2Fq55r6wp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Use**
---
**Statistics and Probability: Confidence Intervals**
4. According to those who know, a sample of 360 one-year-old baby boys in the US had a mean weight of 26.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.
a. **Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the US.**
- **Calculations and Formulas:**
- M = 26.5
- σ = 5.3
- n = 360
- Confidence Level = 95%
- Use the formula for the confidence interval:
\[
\text{Confidence Interval} = \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right)
\]
- Here, \(\bar{x}\) is the sample mean, z is the z-score corresponding to the 95% confidence level (approximately 1.96), and n is the sample size.
b. **Based on the confidence interval level above, is it likely that the mean weight of all one-year-old boys is less than 28 pounds?**
- **Analysis Consideration:**
- Use the constructed confidence interval to determine if 28 pounds is within this range.
- If 28 pounds is above the upper bound of the interval, it suggests that it is unlikely for the mean weight to be less than 28 pounds.
**Diagrams and Mathematical Notations:**
- The handwritten notes on the paper show sample calculations, such as:
- M = 26.5
- σ = 5.3
- Calculations involving the z-score for a 95% confidence interval.
Note: Ensure that when conducting your own calculations, all steps are clearly shown to maintain accuracy and clarity.
---
This information is intended to help users understand how to construct and interpret confidence intervals for statistical analysis.
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