Question

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that = 7.00 ml/kg for the distribution of blood plasma.

Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limit:
upper limit:
margin of error:

Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.10 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

Answer 1

Rounding up to the nearest whole number, you would need a sample size of approximately 327 male firefighters for a 99% confidence level with a maximum margin of error of 2.10 ml/kg.

Explanation:

n = (2.576² * 7.00²) / (2.10²)

n ≈ (6.639776 * 49) / 4.41

n ≈ 326.35

Rounding up to the nearest whole number, you would need a sample size of approximately 327 male firefighters for a 99% confidence level with a maximum margin of error of 2.10 ml/kg.