Please show necessary work Diagnostic Tests Plasma Volume To

Diagnostic Tests: Plasma Volume Total plasma volume is important in deter-mining the required plasma component in blood replacement therapy for a per-son undergoing surgery. Plasma volume is influenced by the overall health and physical activity of individual. (Reference: See Problem 12.) 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 per kilogram body weight). Assume that sigma = 7.50 ml/kg it 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

Solution

(a) Given a=0.01, Z(0.005) =2.58 (from standard normal table)

So the margin of error is

Z*s/vn= 2.58*7.5/sqrt(45)=2.884528

So the lower bound is

xbar - Z*s/vn =37.5-2.884528 =34.61547

So the upper bound is

xbar +Z*s/vn =37.5+2.884528 =40.38453

----------------------------------------------------------------------------------------------------------

(b)We need to assume that the population follows normal distribution.

----------------------------------------------------------------------------------------------------------

(c) We have 99% confident that the population mean will be within this interval.

----------------------------------------------------------------------------------------------------------
(d)

n=(Z*s/E)^2

=(2.58*7.5/2.5)^2

=59.9076

Take n=60