Questions: Babies: 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=5.1 pounds. Part 1 of 3 (a) Construct a 99.5% 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. A 99.5% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <μ<.

Solution Steps

We are provided with the following data regarding a sample of one-year-old baby boys in the United States:

• Sample size (\(n\)) = 360
• Sample mean weight (\(\bar{x}\)) = 25.5 pounds
• Population standard deviation (\(\sigma\)) = 5.1 pounds
• Confidence level = 99.5%

For a confidence level of 99.5%, we need to find the corresponding Z-score. The Z-score for a two-tailed test at this confidence level is approximately \(z = 2.8\).

The standard error (SE) is calculated using the formula: \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{5.1}{\sqrt{360}} \approx 0.2739 \]

The confidence interval is calculated using the formula: \[ \bar{x} \pm z \cdot SE \] Substituting the values: \[ 25.5 \pm 2.8 \cdot 0.2739 \] Calculating the margin of error: \[ 2.8 \cdot 0.2739 \approx 0.765 \] Thus, the confidence interval becomes: \[ (25.5 - 0.765, 25.5 + 0.765) = (24.735, 26.265) \]

Rounding the values to one decimal place, we get: \[ (24.7, 26.3) \]

Final Answer