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 46 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 = 7.80 ml/kg for the distribution of blood plasma.

(a) Find the margin of error for a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Round your answer to two decimal places.)

(B) Find a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.)

(C) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

Answer 1

The margin of error for a 99% confidence interval for the population mean blood plasma volume in male firefighters is approximately 2.68 ml/kg.

Step-by-step explanation:

To find the margin of error for a 99% confidence interval, we need to use the formula:

Margin of Error = Z * (Standard Deviation / sqrt(n))

Where:

Z is the z-score for the desired confidence level, which corresponds to 99% confidence level.

Standard Deviation = $7.80 ml/kg$

n is the sample size.

Using the formula, we can calculate the margin of error:

Margin of Error = Z * (Standard Deviation / sqrt(n))

= 2.33 * ($7.80 ml/kg$ / sqrt(46))

≈ 2.33 * 1.1493

≈ 2.68 ml/kg