Question

A nurse at a local hospital is interested in estimating the birth weights of infants. How large of a sample must she select if she desires to be 90% confident that the true mean is within 4 ounces of the sample mean?

Answer 1

To calculate the required sample size for estimating birth weights with 90% confidence within 4 ounces, the standard deviation is needed. Without it, a preliminary study should be performed to approximate this value, which can then be used with the z-score for 90% confidence in the sample size formula.

Step-by-step explanation:

To determine the required sample size for the nurse to estimate the birth weights of infants with a desired confidence level, we need to know the population standard deviation. If we consider a similar approach to the given reference scenario for elephant calves, we would need the standard deviation for the weights of infants. However, in the absence of that information, we can't calculate the exact sample size.

If the population standard deviation is known, we would apply the formula for the sample size calculation for estimating a population mean, which is n = (Z² * σ²) / E², where Z is the z-score corresponding to the confidence level, σ is the population standard deviation, and E is the margin of error (in this case, 4 ounces). The z-score for a 90% confidence level is typically 1.645. Without the standard deviation, it's recommended that the nurse conduct a preliminary study to estimate this value, which can then be used in the sample size formula.