Babies: According to a recent report, a sample of 240 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is o=5.2 pounds. Part: 0/3 Part 1 of 3 decimal place. (a) Construct a 99.8% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one A 99.8% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is Next Part m Breaking news Get caught up Q Search •MA. 579 X <με Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 93 10/2
Babies: According to a recent report, a sample of 240 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is o=5.2 pounds. Part: 0/3 Part 1 of 3 decimal place. (a) Construct a 99.8% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one A 99.8% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is Next Part m Breaking news Get caught up Q Search •MA. 579 X <με Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 93 10/2
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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![**Title: Statistical Analysis of Infant Weight in the United States**
---
**Introduction to Confidence Intervals**
In a recent study, researchers analyzed the weights of one-year-old baby boys in the United States. From a sample of 2,400 subjects, the mean weight was found to be 25.5 pounds. The study utilized a standard deviation of 5.2 pounds to calculate confidence intervals.
---
**Analysis and Calculations**
**Question:**
Using the data provided, construct a 99% confidence interval for the mean weight of all one-year-old baby boys in the United States. Please round your answer to at least one decimal place.
**Methodology:**
To calculate the confidence interval, the following steps were applied:
1. Identify the sample mean (\(\bar{x}\)) = 25.5 pounds
2. Recognize the standard deviation (\(\sigma\)) = 5.2 pounds
3. Determine the sample size (\(n\)) = 2,400
**Formula for Confidence Interval:**
The formula for a confidence interval is:
\[\bar{x} \pm Z \left(\frac{\sigma}{\sqrt{n}}\right)\]
Where \(Z\) is the Z-score corresponding to the desired confidence level (99%).
**Steps:**
- Calculate the standard error (SE): \(\frac{\sigma}{\sqrt{n}}\)
- Multiply the standard error by the Z-score to find the margin of error.
- Add and subtract the margin of error from the sample mean to get the confidence interval.
**Visualization:**
A basic graph or diagram would illustrate the normal distribution curve, showing the confidence interval as a range around the mean weight (25.5 pounds), with markers indicating the upper and lower bounds.
---
**Conclusion**
Understanding confidence intervals helps in predicting the probable range of values for population parameters. This analysis provides insights into the average weight range for one-year-old boys in the U.S., facilitating better health and nutrition planning.
---
**Next Steps:**
For further study, review statistical texts on hypothesis testing and advanced probability distributions to deepen your understanding of these concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccfc4c36-f702-4d8a-8b8a-bce7b3a6d127%2F5afe3e29-6ac0-49fb-be4b-739bd6481180%2Far1vo8s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Statistical Analysis of Infant Weight in the United States**
---
**Introduction to Confidence Intervals**
In a recent study, researchers analyzed the weights of one-year-old baby boys in the United States. From a sample of 2,400 subjects, the mean weight was found to be 25.5 pounds. The study utilized a standard deviation of 5.2 pounds to calculate confidence intervals.
---
**Analysis and Calculations**
**Question:**
Using the data provided, construct a 99% confidence interval for the mean weight of all one-year-old baby boys in the United States. Please round your answer to at least one decimal place.
**Methodology:**
To calculate the confidence interval, the following steps were applied:
1. Identify the sample mean (\(\bar{x}\)) = 25.5 pounds
2. Recognize the standard deviation (\(\sigma\)) = 5.2 pounds
3. Determine the sample size (\(n\)) = 2,400
**Formula for Confidence Interval:**
The formula for a confidence interval is:
\[\bar{x} \pm Z \left(\frac{\sigma}{\sqrt{n}}\right)\]
Where \(Z\) is the Z-score corresponding to the desired confidence level (99%).
**Steps:**
- Calculate the standard error (SE): \(\frac{\sigma}{\sqrt{n}}\)
- Multiply the standard error by the Z-score to find the margin of error.
- Add and subtract the margin of error from the sample mean to get the confidence interval.
**Visualization:**
A basic graph or diagram would illustrate the normal distribution curve, showing the confidence interval as a range around the mean weight (25.5 pounds), with markers indicating the upper and lower bounds.
---
**Conclusion**
Understanding confidence intervals helps in predicting the probable range of values for population parameters. This analysis provides insights into the average weight range for one-year-old boys in the U.S., facilitating better health and nutrition planning.
---
**Next Steps:**
For further study, review statistical texts on hypothesis testing and advanced probability distributions to deepen your understanding of these concepts.
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