A nurse 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 90% confident that the mean is within 3 ounces of the sample mean? The standard deviation of the birth weghts is known to be 8ounces. Assume the populattion is normally distributed. ( Round your answer up to the nearest whole number)
To determine the sample size required, we can use the formula for the confidence interval for a population mean:
n = (Z * σ / E) ^ 2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = standard deviation of the population
E = margin of error
In this case, the nurse wants to be 90% confident that the mean is within 3 ounces of the sample mean, and the standard deviation of the birth weights is known to be 8 ounces. We need to calculate the Z-score corresponding to a 90% confidence level.
The Z-score can be found using a standard normal distribution table or a calculator. For a 90% confidence level, the Z-score is approximately 1.645.
Using the formula:
n = (1.645 * 8 / 3) ^ 2
n = (13.16 / 3) ^ 2
n = 4.39 ^ 2
n = 19.2721
Rounding up to the nearest whole number:
n = 20
Therefore, the nurse must select a sample size of at least 20 infants to be 90% confident that the mean is within 3 ounces of the sample mean.