Diagnostic Plasma Volume Total plasma volume is important in determining the req
ID: 3218282 • Letter: D
Question
Diagnostic Plasma Volume 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 45 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma kilogram body weight). Assume that sigma = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (b) What conditions are necessary for your calculations? (c) Give a brief interpretation of your results in the context of this problem. (d) Sample Size: Find the sample size necessary for a 99% confidence level with maximal error of estimate E = 2.50 for the mean plasma volume in male firefighters.Explanation / Answer
a) x = 37.5, = 7.50, n = 45, For 99% CI z* = 2.58
CI = x +- (z*)*/sqrt(n)
lower bound = 37.5 - 2.58*7.50/sqrt(45) = 34.615
upper bound = 37.5 + 2.58*7.50/sqrt(45) = 40.385
Margin of Error = (z*)*/sqrt(n) = 2.58*7.5/sqrt(45) = 2.885
b) is known, since n is large(n>=30) central limit theorem lets us assume the sampling distribtuion is very close to normal.
c) There is a 99% chance that the interval 34.6 and 40.4 contains the true population mean of plasma volume
d) (z*)*/sqrt(n) = 2.50
n = ((z*)*/2.50)2 = (2.58*7.5/2.5)2=59.9 = 60samples