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Let's analyze this problem step by step.

### Given Information:
1. **Sample Size (n)** = 360
2. **Sample Mean (\(\bar{x}\))** = 25.5 pounds
3. **Population Standard Deviation (\(\sigma\))** = 5.3 pounds
4. **Confidence Level** = 95%

### Part (a) Solution Verification:
The question for Part (a) was to construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States.

To calculate a confidence interval, we use the formula for the margin of error in a confidence interval:

\[
\text{Margin of Error} = z \times \frac{\sigma}{\sqrt{n}}
\]

Where:
- \(z\) is the z-score corresponding to a 95% confidence level (approximately 1.96).
- \(\sigma\) is the population standard deviation.
- \(n\) is the sample size.

Let's calculate this:

1. **Standard Error (SE)**:
   \[
   SE = \frac{5.3}{\sqrt{360}} \approx 0.28
   \]

2. **Margin of Error**:
   \[
   \text{Margin of Error} = 1.96 \times 0.28 \approx 0.55
   \]

3. **Confidence Interval**:
   \[
   \text{Confidence Interval} = \bar{x} \pm \text{Margin of Error} = 25.5 \pm 0.55
   \]

   Therefore, the confidence interval is approximately:
   \[
   (24.9, 26.0)
   \]

This matches the answer shown in Part (a).

### Part (b) Explanation:
The question in Part (b) asks whether this confidence interval can be used to estimate the mean weight of all one-year-old babies in the United States.

Since the sample was taken from one-year-old baby boys only, this confidence interval specifically estimates the mean weight for one-year-old **baby boys**, not all one-year-old babies in general (which would include both boys and girls). Thus, it **should not** be used to generalize for all one-year-old babies in the United States.

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Would you like further details on any part of the solution, or have any questions?

### Related Questions:
1. How do we determine the z-score for different confidence levels?
2. What if we didn’t know the population standard deviation; how would the calculation change?
3. Why is it incorrect to generalize results from a sample of boys to all babies?
4. What other statistical methods can estimate population parameters?
5. How would the interval change if the sample size were smaller?

### Tip:
For larger sample sizes, the confidence interval becomes narrower, giving a more precise estimate of the population mean.

According to a recent report, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 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 United States. Round the answer to at least one decimal place. (b) Should this confidence interval be used to estimate the mean weight of all one-year-old babies in the United States? Explain.

Learn how to calculate a 95% confidence interval for the mean weight of one-year-old baby boys in the United States, given a sample of 360 boys with an average weight of 25.5 pounds and a population standard deviation of 5.3 pounds. This solution includes step-by-step instructions for calculating the confidence interval and explains its limitations when generalizing to all one-year-old babies.

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