Question

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 true mean is within 3 ounces of the sample mean? The standard deviation of the birth weights is known to be 9 ounces.

Answer 1

To estimate infant birth weights within 3 ounces with 90% confidence, using a known population standard deviation of 9 ounces, the nurse needs a sample size of at least 25 infants.

Step-by-step explanation:

To determine the sample size needed to estimate the birth weight of infants with a desired confidence level, we use the formula for sample size in estimating a population mean when the population standard deviation is known:

n = (Z·σ/E)^2

Where n is the sample size, Z is the Z-score associated with the confidence level, σ is the population standard deviation, and E is the margin of error.

In this case, the nurse wants to be 90% confident that the true mean is within 3 ounces of the sample mean. The known standard deviation (σ) is 9 ounces. The Z-score associated with a 90% confidence level is approximately 1.645 (this value can be found using a Z-table or standard normal distribution table).

Plugging in the values we get:

n = (1.645· 9/3)^2

n = (1.645· 3)^2

n = (4.935)^2

n = 24.36

Since the sample size must be a whole number, we would round up to the nearest whole number, so the nurse would need a sample size of at least 25 infants to meet her criteria for the estimate.