**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 pounds2. Recognize the standard deviation ($\sigma$) = 5.2 pounds3. 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.

n=240,x¯=25.5,σ=5.2C.I=99.8%=0.998α=1−C.I=1−0.998=0.002

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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Question

100%

**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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