Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error
-A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 98% confident that the true mean is within 2 ounces of the sample mean The standard deviation of the birth weights is known to be 8 ounces.
A) 87
B) 86
C) 10
D) 9

Question

Quizplus · Accepted Answer

To determine the sample size necessary for estimating the population mean within a specified margin of error, we use the formula: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 98% confidence level, the Z-score is approximately 2.33. Given $\sigma = 8$ ounces and $E = 2$ ounces, substituting these values into the formula gives $n = \left(\frac{2.33 \cdot 8}{2}\right)^2 = 86.49$. Since the sample size must be a whole number, we round up to the nearest whole number, which is 87.