A healthcare professional wants to estimate the mean birth weight of infants born to mothers who take a certain vitamin while pregnant. How large a sample must she take in order to be 95% confident that the error is at most .6 pounds? Assume the population standard deviation can be approximated to be 3.8 pounds.
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To estimate the required sample size, the healthcare professional can use the formula for calculating the sample size for estimating a population mean:
n = (Z * σ / E)^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 95% confidence level)
σ = population standard deviation
E = desired margin of error
In this case, the desired margin of error (E) is 0.6 pounds, and the population standard deviation (σ) is 3.8 pounds. The Z-score for a 95% confidence level is approximately 1.96.
Substituting these values into the formula:
n = (1.96 * 3.8 / 0.6)^2
n = (7.328 / 0.6)^2
n = 12.213^2
n ≈ 148.92
Therefore, the healthcare professional needs to take a sample size of approximately 149 in order to be 95% confident that the error is at most 0.6 pounds.