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 =σ5.2 pounds.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(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 decimal place.A 99.8% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <<μ.
Question
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 =σ5.2 pounds.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(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 decimal place.A 99.8% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <<μ.
Solution
To construct a 99.8% confidence interval for the mean weight of all one-year-old baby boys in the United States, we will use the formula for a confidence interval:
CI = X ± Z * (σ/√n)
where:
- X is the sample mean
- Z is the Z-score corresponding to the desired confidence level
- σ is the population standard deviation
- n is the sample size
Given in the problem, we have:
- X = 25.5 pounds
- σ = 5.2 pounds
- n = 240
The Z-score for a 99.8% confidence level is approximately 3.09 (you can find this value in a standard Z-table or using a calculator that provides this function).
Substituting these values into the formula, we get:
CI = 25.5 ± 3.09 * (5.2/√240)
Calculating the value inside the parenthesis:
5.2/√240 ≈ 0.336
Then multiply by the Z-score:
3.09 * 0.336 ≈ 1.038
So, the confidence interval is:
CI = 25.5 ± 1.038
Therefore, we can be 99.8% confident that the true mean weight of all one-year-old baby boys in the United States is between 24.5 pounds and 26.5 pounds, rounded to one decimal place.
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