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 σ = 7.00 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.)

the distribution of weights is normal

the distribution of weights is uniform

σ is known

σ is unknown

n is large

(c) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

____ male firefighters

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 37.5

Population standard deviation =    = 7.00

Sample size = n = 46

a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

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

E = 2.576 * (7.00 /  46 )

E = 2.66

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

  ± E

37.5 ± 2.66

( 34.84, 40.16)  

lower limit = 34.84

upper limit = 40.16

margin of error = 2.66

b) the distribution of weights is normal

σ is known

n is large

c) margin of error = E = 2.00

sample size = n = [Z_/2* / E] ²

n = [2.576 *7.00 / 2.00]²

n = 81.28

Sample size = n = 82 male firefighters