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 =σ5.1 pounds.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Construct an 80% 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.An 80% 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 =σ5.1 pounds.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Construct an 80% 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.An 80% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <<μ.
Solution
To construct an 80% confidence interval for the mean weight of all one-year-old baby boys in the United States, we first need to find the standard error. The standard error (SE) is calculated by dividing the standard deviation (σ) by the square root of the sample size (n).
In this case, the standard deviation (σ) is 5.1 pounds and the sample size (n) is 240.
SE = σ / √n = 5.1 / √240 = 0.329
Next, we need to find the z-score that corresponds to an 80% confidence level. The z-score for an 80% confidence level is 1.28 (you can find this value in a standard z-table or use a calculator that provides this value).
The margin of error (E) is then calculated by multiplying the z-score by the standard error.
E = z * SE = 1.28 * 0.329 = 0.421
Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample mean.
Lower limit = mean - E = 25.5 - 0.421 = 25.1 Upper limit = mean + E = 25.5 + 0.421 = 25.9
So, an 80% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is (25.1, 25.9).
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