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 41 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 σ = 7.10 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? (Round your answers to two decimal places.)

lower limit
upper limit
margin of error

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is large

σ is known

σ is unknown

the distribution of weights is uniform

the distribution of weights is normal

Answer 1

Solution :

Z/2 = Z_0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

E = 2.576 * ( 7.10 /  41 )

E = 2.86

At 99% confidence interval estimate of the population mean is,

  ± E

= 37.5  ± 2.86

= ( 34.64, 40.36 )

lower limit = 34.64

upper limit = 40.36

margin of error = 2.86

b) n is large

σ is known